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Resources

Compare linear and exponential growth

h(t)=-16.1 t^{2}+5 t+32.4

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Mark is tossing a set of keys from his balcony to his friends below. The function models

h

, the height of the keys in feet

t

seconds after the toss. What is the initial height of the keys in feet?

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1

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0

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5

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16

1

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32

4

6^{\frac{1}{2}}+6^{\frac{3}{2}}

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Which of the following values is equal to the given value?

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1

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\sqrt{222}

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7 \sqrt{6}

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6^{\frac{3}{4}}

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36

\frac{\left(\frac{l^{5} m^{4} n^{6}}{p q}\right)}{\left(\frac{l^{5} m^{3} n^{6}}{p^{2} q^{2}}\right)}

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Which expression is equivalent to the given quotient for all

m, n, p, q>0

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1

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\frac{1}{m p q}

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m p q

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\frac{l^{10} m^{7} n^{12}}{p^{3} q^{3}}

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1

\sqrt[3]{x^{2}} \cdot x^{-\frac{1}{5}}

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Which of the following is equivalent to the given expression for all real values of

x

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1

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\sqrt[15]{x^{7}}

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\sqrt[7]{x^{15}}

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\frac{1}{\sqrt{x^{15}}}

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\frac{1}{\sqrt[15]{x^{2}}}

\left(\frac{a^{7}}{a^{-3}}\right)^{0} \cdot \frac{a^{3}\left(a^{-2}\right)^{4}}{a^{7}}

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The given expression simplifies to

a^{x}

, for some integer

x

. What is the value of

x

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1

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-12

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0

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2

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12

\left(b^{\frac{3}{4}}\right)^{\frac{2}{9}}

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Which of the following expressions is equivalent to the given expression?

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1

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\sqrt{b^{6}}

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\frac{2}{9} \sqrt[4]{b^{3}}

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\sqrt[13]{b^{5}}

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\sqrt[6]{b}

\left(\frac{64}{b^{27}}\right)^{-\frac{2}{3}}

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Which of the following is equivalent to the given expression?

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1

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\frac{b^{9}}{16}

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\frac{b^{18}}{16}

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-\frac{128 b^{9}}{3}

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-\frac{128 b^{18}}{3}

\left(\frac{1}{8}\right)^{-\frac{2}{3}}

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What is the value of the given expression?

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1

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-\frac{1}{12}

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\frac{1}{4}

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4

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12

\left(\frac{j^{15}}{8}\right)^{\frac{2}{3}}

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Which of the following expressions is equivalent to the given expression?

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1

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\frac{j^{10}}{4}

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\frac{j^{30}}{512}

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\frac{j^{10}}{8}

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\frac{j^{30}}{8}

\frac{a^{2} a^{-5}}{a^{-3} a^{0}} \cdot\left(\frac{a^{2}}{a^{3}}\right)^{-4}=a^{x}

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What is the value of

x

\frac{\left(\frac{2 m c^{2}}{6 b}\right)}{\left(\frac{10 c^{4}}{3 b^{3}}\right)}

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Which expression is equivalent to the given quotient for all

b>0

c>0

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1

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\frac{m}{10}

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\frac{m b^{2}}{10 c^{2}}

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\frac{5 m c^{2}}{16 b^{2}}

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\frac{10 m c^{6}}{9 b^{4}}

\frac{\left(\frac{10 p}{9 r^{5}}\right)}{\left(\frac{5 p^{7}}{3 r^{2}}\right)}

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Which expression is equivalent to the given quotient for all

p>2

r<-2

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1

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\frac{2}{3 r^{3} p^{6}}

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\frac{2 p^{6}}{3 r^{3}}

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\frac{3 r^{3} p^{6}}{2}

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\frac{3 r^{3}}{2 p^{6}}

Which of the following is equivalent to

\left(2 x^{3} y^{4} z^{5}\right)^{3}

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1

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6 x^{9} y^{12} z^{15}

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8 x^{9} y^{12} z^{15}

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6 x^{6} y^{7} z^{8}

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8 x^{6} y^{7} z^{8}

\left(2 y^{2} z^{10}\right)^{5}

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Which of the following expressions is equivalent to the given expression?

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1

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10 y^{32} z^{100,000}

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10 y^{10} z^{50}

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32 y^{32} z^{100,000}

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32 y^{10} z^{50}

\frac{24}{O+P}=5

, which of the following correctly expresses

O

P

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1

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O=\frac{5}{24}-P

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O=\frac{24}{5}-P

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O=\frac{24}{5}+P

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O=120-P

\frac{P+R}{2}=8

, which of the following correctly gives

R

P

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1

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R=16+P

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R=16-P

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R=8-\frac{P}{2}

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R=4-P

Q-\frac{1}{3} P=30

, which of the following correctly gives

P

Q

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1

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P=Q-90

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P=Q-30

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P=3 Q-90

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P=3 Q-30

3 c-5=d

, which of the following correctly gives

c

d

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1

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c=\frac{d-5}{3}

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c=\frac{d+5}{3}

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c=3 d-5

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c=3 d+15

g(x)=2 x^{2}+x

, what is the value of

g\left(\frac{1}{2}\right)

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1

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\frac{1}{2}

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1

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\frac{3}{2}

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\frac{5}{2}

g(x)=\frac{10}{x^{2}}

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g

is defined. What is the value of

g(5)

f(x)=x^{2}-6 x-8

, what is the value of

f(-2)

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1

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-16

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-10

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0

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8

h(x)=x^{2}+3 x+1

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h

is defined. What is the value of

h(3)

p(x)=(0.6)\left(3^{x}\right)

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p

is defined. What is the value of

p(2)

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1

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1

8

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3

6

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5

4

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9

f(x)=\left(\frac{1}{4}\right)^{x}

, what is the value of

f(3)

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1

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\frac{3}{4}

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\frac{1}{16}

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\frac{1}{64}

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\frac{1}{256}

f(x)=x^{3}+2 x+7

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f

is defined. What is the value of

f(-3)

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1

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-26

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-14

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10

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40

h(x)=\frac{1}{x^{2}-1}

, what is the value of

h(3)

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1

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\frac{1}{8}

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\frac{1}{4}

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\frac{1}{3}

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\frac{1}{2}

\left(t+\frac{1}{3}\right)\left(t+\frac{2}{3}\right)=0

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What are the solutions to the given equation?

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1

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t=-\frac{2}{3}

t=-\frac{1}{3}

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t=-\frac{2}{3}

t=\frac{2}{3}

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t=-\frac{1}{3}

t=\frac{1}{3}

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t=\frac{1}{3}

t=\frac{2}{3}

0=32-50 x^{2}

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What are the solutions to the given equation?

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1

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x=\frac{4}{5}

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x=-\frac{4}{5}

x=\frac{4}{5}

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x=\frac{16}{25}

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x=-\frac{16}{25}

x=\frac{16}{25}

f(t)=14(0.85)^{t}

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The function models

f

, the value of a professional quality video camera, in thousands of dollars,

t

years after its purchase. What is the value of the camera at the time of purchase?

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1

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\$ 11,900

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\$ 14,000

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\$ 15,000

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\$ 85,000

\frac{\left(\frac{a}{b}\right)}{c} \cdot \frac{a}{\left(\frac{b}{c}\right)}

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Which of the following is equivalent to the given expression?

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1

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\frac{a^{2}}{b^{2}}

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\frac{a^{2}}{c^{2}}

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\frac{a^{2}}{b^{2} c^{2}}

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\frac{a^{2} c^{2}}{b^{2}}

a \neq 0

, which of the following expressions is equivalent to

\frac{-12 a^{2}+96 a}{-12 a^{2}+60 a}

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1

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\frac{-a+8}{-a-5}

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\frac{a+8}{-a+5}

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\frac{-a+8}{-a+5}

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\frac{-a+8 a}{-a+5 a}

Which of the following expressions is equivalent to

\frac{\left(\frac{2}{x+y}\right)}{\left(\frac{x+y}{2}\right)}

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1

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x+y

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1

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\frac{4}{(x+y)^{2}}

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\frac{x+y}{2}

\frac{5 m^{2}+7 m}{2 m-9}-\frac{2 m}{2 m-9}

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Which expression is equivalent to the difference?

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1

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\frac{3 m^{2}+7 m}{2 m-9}

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\frac{5 m^{2}+5 m}{2 m-9}

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\frac{5 m+9 m}{2 m-9}

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\frac{5 m^{2}+7 m-1}{2 m-9}

\frac{\left(\frac{a}{b}\right)}{c}+\frac{d}{\left(\frac{e}{f}\right)}

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Which of the following is equivalent to the expression above?

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1

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\frac{a}{b c}+\frac{d f}{e}

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\frac{a}{b c}+\frac{d e}{f}

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\frac{b c}{a}+\frac{d f}{e}

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\frac{b c}{a}+\frac{d e}{f}

\frac{x^{3}+9 x^{2}}{x^{3}}

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Which expression is equivalent to the given expression for all

x>1

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1

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9 x^{2}

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1+9 x^{2}

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\frac{x+9}{x}

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\frac{1+9 x}{x}

t \neq 0

, which of the following expressions is equivalent to

\frac{81 t^{2}+27 t}{9 t^{2}+9 t}

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1

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\frac{9 t+27}{t+9}

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\frac{9 t+3 t}{t+1 t}

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\frac{9 t+3}{t+1}

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\frac{9 t+9}{t+3}

y \neq 0

, which of the following expressions is equivalent to

\frac{56 y^{2}-28 y}{35 y^{2}+21 y}

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1

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\frac{8 y-4}{5 y-3}

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\frac{8 y-4 y}{5 y+3 y}

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\frac{8 y-28}{5 y+21}

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\frac{8 y-4}{5 y+3}

r \neq 0

, which of the following expressions is equivalent to

\frac{-24 r^{2}-56 r}{-48 r^{2}+64 r}

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1

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\frac{-3 r+7}{-6 r+8}

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\frac{-3 r-7 r}{-6 r+8 r}

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\frac{3 r+7}{-6 r+8}

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\frac{-3 r-7}{-6 r+8}

y=f(x)

is a parabola in the

x y

-plane that is symmetric with respect to the line

x=-2

y

-coordinate of the vertex of the graph of

f

is a maximum function value. Which of the following equations could represent function

f

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1

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f(x)=5(x-2)^{2}+3

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f(x)=5(x+2)^{2}+3

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f(x)=-5(x-2)^{2}+3

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f(x)=-5(x+2)^{2}+3

x-2 y=0

, which of the following correctly gives

y

x

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1

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y=-2 x

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y=-\frac{1}{2} x

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y=\frac{1}{2} x

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y=2 x

\begin{array}{c} y=\frac{4}{7} x \\ \frac{2}{3} x=y+\frac{5}{7} \end{array}

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Consider the system of equations. If

(x, y)

is the solution to the system, then what is the value of

y

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1

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\frac{2}{21}

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\frac{30}{7}

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\frac{15}{2}

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(D) None of the above

In a political science class, test scores were determined to be

20

times the number of hours,

h

, the student studied plus

3

. Which of the following functions best describes a student's test score depending on the number of hours,

h

, that the student studied?

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1

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f(h)=3 h+20

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f(h)=20 h

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f(h)=60 h

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f(h)=20 h+3

200

cakes in preparation for an upcoming holiday. Each cake was made from

4

5

cups of batter and

3

5

cups of frosting. Which of the following shows the number of cups of batter,

b(f)

, the bakery used as a function of the

f

cups of frosting that the bakery used?

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1

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b(f)=\frac{7}{9} f

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b(f)=\frac{200-7 f}{9}

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b(f)=\frac{9}{7} f

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b(f)=\frac{200-9 f}{7}

Gary learned that the value of his car depreciates by

15 \%

of its initial purchase value each year. If the initial purchase value of Gary's car is

m

dollars, which of the following functions best describes the value of his car one year after purchase?

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1

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f(m)=0.15 m

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f(m)=0.85 m

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f(m)=1-0.15 m

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f(m)=1-0.85 m

A cellular phone salesperson earns an annual base salary of

\$ 25,000

. Additionally, the salesperson earns a

10 \%

commission on their total sales. Which of the following functions best models the salesperson's total annual earnings,

E

, when they bill

s

dollars in total sales?

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1

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E(s)=0.10 \cdot 25,000 \cdot s

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E(s)=25,000+0.10 s

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E(s)=0.10+25,000 s

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E(s)=\frac{25,000}{0.10} s

The temperature in kelvin,

K

\frac{5}{9}

times the sum of

459

67

and the temperature in degrees Fahrenheit,

F

. Which of the following equations best describes the relationship between temperature in kelvin and degrees Fahrenheit?

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1

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K=\frac{5}{9} \cdot 459.67+F

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K=459.67+\frac{5}{9} F

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K=\frac{5}{9}(459.67+F)

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K=459.67\left(\frac{5}{9}+F\right)

\begin{array}{l}h(x)=\left\{\begin{array}{ll}\frac{1}{x-5} & , \quad x=0 \\ -(x-4)^{2} & , \quad x=7 \\ 3 x-2 & , \quad x \neq 0\end{array}\right. \\ h(6)= \\\end{array}

The equation of a circle is

(x+6)^{2}+(y+8)^{2}=1

. What are the center and radius of the circle?

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1

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(A) The center is

(6,-8)

and the radius is

1

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(B) The center is

(-6,8)

and the radius is

1

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(C) The center is

(-6,-8)

and the radius is

1

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D The center is

(6,8)

and the radius is

1

The equation of a circle is

(x+2)^{2}+(y+6)^{2}=16

. What are the center and radius of the circle?

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1

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(A) The center is

(2,-6)

and the radius is

6

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(B) The center is

(-2,6)

and the radius is

6

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(C) The center is

(-2,-6)

and the radius is

4

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(D) The center is

(1,2)

and the radius is

16

The equation of a circle is

(x-9)^{2}+(y+8)^{2}=4

. What are the center and radius of the circle?

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1

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(A) The center is

(9,-8)

and the radius is

2

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(B) The center is

(-9,-8)

and the radius is

2

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(C) The center is

(9,8)

and the radius is

2

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(D) The center is

(9,-8)

and the radius is

4

...