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What kind of transformation converts the graph of $f(x) = -5(x + 2)^2$ into the graph of $g(x) = -5(x + 2)^2 + 4$ ? $\newline$ Choices: $\newline$ (A) translation $4$ units left $\newline$ (B) translation $4$ units up $\newline$ (C) translation $4$ units down $\newline$ (D) translation $4$ units right

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Describe function transformations

Full solution

Q. What kind of transformation converts the graph of

f(x) = -5(x + 2)^2

into the graph of

g(x) = -5(x + 2)^2 + 4

?

\newline

Choices:

\newline

(A) translation

4

units left

\newline

(B) translation

4

units up

\newline

(C) translation

4

units down

\newline

(D) translation

4

units right

Find Vertex of $f(x)$ : Look at the original function $f(x) = -5(x + 2)^2$ . Find the vertex of $f(x)$ . Vertex of $f(x)$ : $(-2, 0)$ because the vertex form is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex.
Find Vertex of g(x): Now look at the transformed function $g(x) = -5(x + 2)^2 + 4$ . Find the vertex of $g(x)$ . Vertex of $g(x)$ : $(-2, 4)$ because adding $4$ only affects the y-coordinate of the vertex.
Compare Vertices: Compare the vertices of $f(x)$ and $g(x)$ . $\newline$ Vertex of $f(x)$ : $(-2, 0)$ $\newline$ Vertex of $g(x)$ : $(-2, 4)$ $\newline$ The $x$ -coordinates are the same, so there's no horizontal shift. $\newline$ The $y$ -coordinate of $g(x)$ is $4$ units higher than $f(x)$ , so it's a vertical shift.
Determine Vertical Shift: Determine the direction of the vertical shift. Since the $y$ -coordinate increased by $4$ , the graph moved up.
Identify Transformation: Identify the transformation. $\newline$ The graph of $f(x)$ moved $4$ units up to become $g(x)$ .

More problems from Describe function transformations

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What does the transformation

f(x) \mapsto f(x) - 6

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f(x)

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\newline

\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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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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\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)

is the reflection across the x-axis of

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

\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

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Question

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

\newline

1

\newline

\frac{1}{2}

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1

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

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(D) The limit doesn't exist.

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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}

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6

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

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7

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

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

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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.

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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

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3

\quad y=\frac{x^{2}}{10}+C

\newline

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

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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

\frac{30}{3 x^{2}+C}

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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|

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|-75+250|

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Question

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

\newline

The function represents a parabola in the

xy

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f

y

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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

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

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

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Determine whether the function

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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

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f(x)

is continuous at

x=-3

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