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If $y=\frac{1}{3}(x-2)^{2}$ is graphed in the $xy$ -plane, which of the following characteristics of the graph are displayed as a constant or coefficient in the equation? $\newline$ I. $x$ -intercept(s) $\newline$ II. $y$ -intercept $\newline$ III. $x$ -coordinate of the line of symmetry $\newline$ Choose $1$ answer: $\newline$ (A) I only $\newline$ (B) I and II only $\newline$ (C) I and III only $\newline$ (D) I, II, and III

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Reflections of functions

Full solution

Q. If

y=\frac{1}{3}(x-2)^{2}

is graphed in the

xy

-plane, which of the following characteristics of the graph are displayed as a constant or coefficient in the equation?

\newline

I.

x

-intercept(s)

\newline

II.

y

-intercept

\newline

III.

x

-coordinate of the line of symmetry

\newline

Choose

1

answer:

\newline

(A) I only

\newline

(B) I and II only

\newline

(C) I and III only

\newline

(D) I, II, and III

Analyze Equation Characteristics: Analyze the equation $y = \frac{1}{3}(x-2)^2$ to determine the characteristics displayed in the equation.
Identify Line of Symmetry: Identify the $x$ -coordinate of the line of symmetry using the vertex form.
Check for X-Intercepts: Check for x-intercepts by setting $y = 0$ and solving for $x$ .
Determine Y-Intercept: Determine the $y$ -intercept by substituting $x = 0$ into the equation.

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What does the transformation

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\text{translates it } 6 \text{ units down}

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\text{translates it } 6 \text{ units right}

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\text{translates it } 6 \text{ units left}

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\text{translates it } 6 \text{ units up}

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Question

g(x)

g(x)

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\text{[g(x) = 4x - 1]}

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\text{[g(x) = -4x + 1]}

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Question

What kind of transformation converts the graph of

f(x) = -8(x - 4)^2 + 6

into the graph of

g(x) = -8(x + 6)^2 + 6

\newline

\newline

\text{[A]translation 10 units left}

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\text{[B]translation 10 units right}

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\text{[C]translation 10 units up}

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\text{[D]translation 10 units down}

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Question

g(x)

g(x)

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\newline

\newline

g(x) = 6(x - 7)^2 - 2

\newline

g(x) = -6(x + 7)^2 + 2

\newline

g(x) = -6(x - 7)^2 - 2

\newline

g(x) = 6(x + 7)^2 - 2

Posted 5 months ago

Question

\lim _{x \rightarrow \frac{\pi}{4}} \cos (x)=?

\newline

1

\newline

\frac{1}{2}

\newline

1

\newline

\frac{\sqrt{2}}{2}

\newline

(D) The limit doesn't exist.

Posted 10 months ago

Question

Tess tried to solve the differential equation

\frac{d y}{d x}=2 x y-6 x

. This is her work:

\newline

\frac{d y}{d x}=2 x y-6 x

\newline

1

\quad \frac{d y}{d x}=(y-3) 2 x

\newline

2

\quad \int \frac{1}{y-3} d y=\int 2 x d x

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3

\quad \ln |y-3|=x^{2}+C_{1}

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4

\quad e^{\ln |y-3|}=e^{x^{2}}+C_{1}

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5

\quad|y-3|=e^{x^{2}}+C_{1}

\newline

6

\quad y-3= \pm e^{x^{2}}+C_{2}

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7

\quad y= \pm e^{x^{2}}+C

\newline

Is Tess's work correct? If not, what is her mistake?

\newline

1

\newline

(A) Tess's work is correct.

\newline

1

is incorrect. We're not allowed to factor an expression when solving differential equations.

\newline

4

is incorrect. The right-hand side of the equation should be

e^{x^{2}+C_{1}}

\newline

7

is incorrect. Tess didn't account for adding

3

to the right side.

Posted 8 months ago

Question

Aditya tried to solve the differential equation

\frac{d y}{d x}=6 x-30

. This is his work:

\newline

\frac{d y}{d x}=6 x-30

\newline

1

\quad \int 30 d y=\int 6 x d x

\newline

2

\quad 30 y=3 x^{2}+C

\newline

3

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\newline

Is Aditya's work correct? If not, what is his mistake?

\newline

1

\newline

(A) Aditya's work is correct.

\newline

1

is incorrect. The separation of variables wasn't done correctly.

\newline

2

is incorrect. Aditya didn't integrate

30

\newline

3

is incorrect. The right-hand side of the equation should be

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Posted 9 months ago

Question

Jonael dropped a sandbag from a hot air balloon at a target that is

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\newline

2

of the following expressions represents the distance between the sandbag and the target?

\newline

2

\newline

|-250+75|

\newline

|250+75|

\newline

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Posted 9 months ago

Question

f(x) = -(x+1)(x+7)

\newline

The function represents a parabola in the

xy

-plane. Which of the following is an equivalent form of

f

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f

appears as a constant or coefficient?

\newline

1

\newline

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

\newline

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

\newline

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\newline

f(x) = -x^{2}-8x-7

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Question

Determine whether the function

f(x)

is continuous at

x=-3

\newline

f(x)=\left\{\begin{array}{ll} 18-x^{2}, & x \leq-3 \\ 15+3 x, & x>-3 \end{array}\right.

\newline

f(x)

is discontinuous at

x=-3

\newline

f(x)

is continuous at

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