Resources

Resources

Nth roots

Liz solved the equation

3(n - 2) = -6 + 4n - n

. Here are her last two steps:

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3n - 6 = -6 + 3n

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-6 = -6

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Which statement is true about the equation?

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(A)The solution is

n = -6

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(B)There is no solution because

-6 = -6

is a true equation.

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(C)There are infinitely many solutions because

-6 = -6

is a true equation.

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(D)The solution is

(-6, 6)

Use the Distributive Property to write an expression equivalent to

4(c+8)

. Use pencil and paper. Write the algebraic expression

4(c+8)

in words. Then write the equivalent expression in words. Describe the similarities and the differences in the two statements.

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(c+8)=

\square

(Simplify your answer.)

f(x)=(2 x-1)(3 x+5)(x+1)

x=-\frac{5}{3}, x=-1

x=\frac{1}{2}

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What is the sign of

f

on the interval

-\frac{5}{3}<x<\frac{1}{2}

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1

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f

is always positive on the interval.

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f

is always negative on the interval.

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f

is sometimes positive and sometimes negative on the interval.

f(x)=x(x+3)(x+1)(x-4)

x=-3, x=-1, x=0

x=4

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What is the sign of

f

on the interval

-1<x<4

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1

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f

is always positive on the interval.

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f

is always negative on the interval.

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f

is sometimes positive and sometimes negative on the interval.

f(x)=(x-1)(4 x+3)(3 x-8)

x=-\frac{3}{4}, x=1

x=\frac{8}{3}

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What is the sign of

f

on the interval

-\frac{3}{4}<x<1

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1

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f

is always positive on the interval.

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f

is always negative on the interval.

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f

is sometimes positive and sometimes negative on the interval.

f(x)=(3 x-2)(x+4)(9 x+5)

x=-4, x=-\frac{5}{9}

x=\frac{2}{3}

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What is the sign of

f

on the interval

-\frac{5}{9}<x<\frac{2}{3}

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1

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f

is always positive on the interval.

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f

is always negative on the interval.

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f

is sometimes positive and sometimes negative on the interval.

f(x)=(5 x+1)(4 x-8)(x+6)

x=-6, x=-\frac{1}{5}

x=2

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What is the sign of

f

on the interval

-\frac{1}{5}<x<2

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1

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f

is always positive on the interval.

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f

is always negative on the interval.

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f

is sometimes positive and sometimes negative on the interval.

f(x)=(2 x-1)(3 x-5)(x-4)(3 x+6)

x=-2, x=\frac{1}{2}, x=\frac{5}{3}

x=4

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What is the sign of

f

on the interval

\frac{1}{2}<x<\frac{5}{3}

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1

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f

is always positive on the interval.

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f

is always negative on the interval.

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f

is sometimes positive and sometimes negative on the interval.

The polynomial function

f

f(c)=(c-k)(c^{2}-4c+4)

k

is a constant. The value

2

f

. What is the remainder of

f(c)

when divided by

(c-2)?

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Given the function

f(x)=-5 x-1

f(x)-1

as a simplified polynomial?

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-90^{\circ} \leq \theta \leq 90^{\circ}

. Find the value of

\theta

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\begin{array}{l} \sin (\theta)=-\frac{\sqrt{3}}{2} \\ \theta=\square^{\circ} \end{array}

State why the following expression is not a polynomial.

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4 \mathrm{x}^{-1}+6 \mathrm{x}

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Choose the correct answer below.

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A. The exponent of the variable is a rational number.

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B. The exponent of the variable is a negative integer.

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C. The expression is a quotient of polynomials, which cannot be simplified to a polynomial.

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D. The exponent of the variable is an irrational number.

f

be a twice differentiable function, and let

f(1)=-7

f^{\prime}(1)=0

f^{\prime \prime}(1)=-2

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What occurs in the graph of

f

(1,-7)

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1

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(1,-7)

is a minimum point.

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(1,-7)

is a maximum point.

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(C) There's not enough information to tell.

f

be a twice differentiable function, and let

f(-3)=-4

f^{\prime}(-3)=0

f^{\prime \prime}(-3)=1

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What occurs in the graph of

f

(-3,-4)

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1

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(-3,-4)

is a minimum point.

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(-3,-4)

is a maximum point.

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(C) There's not enough information to tell.

f(x)=\frac{6 x+5}{2-\sqrt{14+5 x}}

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We want to find

\lim _{x \rightarrow-2} f(x)

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What happens when we use direct substitution?

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1

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(A) The limit exists, and we found it!

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(B) The limit doesn't exist (probably an asymptote).

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(C) The result is indeterminate.