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What kind of transformation converts the graph of $f(x) = 5(x - 2)^2 + 4$ into the graph of $g(x) = 5(x + 5)^2 + 4$ ? $\newline$ Choices: $\newline$ (A) translation $7$ units down $\newline$ (B) translation $7$ units up $\newline$ (C) translation $7$ units left $\newline$ (D) translation $7$ 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 + 4

into the graph of

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

?

\newline

Choices:

\newline

(A) translation

7

units down

\newline

(B) translation

7

units up

\newline

(C) translation

7

units left

\newline

(D) translation

7

units right

Identify Vertex: Identify the vertex of the function $f(x) = 5(x - 2)^2 + 4$ . $\newline$ The vertex form of a quadratic function is $f(x) = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. For $f(x) = 5(x - 2)^2 + 4$ , the vertex is at $(h, k) = (2, 4)$ .
Identify Vertex: Identify the vertex of the function $g(x) = 5(x + 5)^2 + 4$ . $\newline$ Similarly, for $g(x) = 5(x + 5)^2 + 4$ , the vertex is at $(h, k) = (-5, 4)$ .
Determine Horizontal Shift: Determine the horizontal shift between the vertices of $f(x)$ and $g(x)$ . The horizontal shift is the difference in the $x$ -coordinates of the vertices. The $x$ -coordinate of the vertex of $f(x)$ is $2$ , and the $x$ -coordinate of the vertex of $g(x)$ is $-5$ . The shift is from $2$ to $-5$ , which is a shift of $g(x)$ $1$ units to the left.
Determine Vertical Shift: Determine if there is any vertical shift between the vertices of $f(x)$ and $g(x)$ . The vertical shift is the difference in the $y$ -coordinates of the vertices. Since both $y$ -coordinates are $4$ , there is no vertical shift.

More problems from Describe function transformations

Question

g(x)

g(x)

is the reflection across the x-axis of

f(x)=9|x+2|-4

\newline

\newline

\text{}(A)g(x) = 9|x+2| - 4\text{]}

\newline

\text{}(B)g(x) = 9|x-2| - 4\text{]}

\newline

\text{}(C)g(x)=-9|x-2| +4\text{]}

\newline

\text{(D)}g(x) = -9|x + 2| + 4\text{]}

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What does the transformation

f(x) \mapsto f(x - 4)

do to the graph of

f(x)

\newline

\newline

\text{translates it } 4 \text{ units right}

\newline

\text{translates it } 4 \text{ units down}

\newline

\text{translates it } 4 \text{ units left}

\newline

\text{translates it } 4 \text{ units up}

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What does the transformation

f(x) \mapsto f(4x)

do to the graph of

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\newline

\newline

[A] stretches it vertically

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[B] stretches it horizontally

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[C]shrinks it horizontally

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[D]shrinks it vertically

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Question

g(x)

g(x)

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f(x) = 10x + 8

\newline

\newline

g(x) = 10x - 82

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g(x) = 10x + 98

\newline

g(x) = 10x - 1

\newline

g(x) = 10x + 17

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Question

What kind of transformation converts the graph of

f(x) = -3x^2 - 4

into the graph of

g(x) = -3x^2 + 6

\newline

\newline

\text{[A]translation 10 units up}

\newline

\text{[B]translation 10 units down}

\newline

\text{[C]translation 10 units left}

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\text{[D]translation 10 units right}

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Question

y=x^{2}

is scaled vertically by a factor of

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. What is the equation of the new parabola?

\newline

y=

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y=x^{2}

is shifted down by

6

units and to the right by

5

\newline

What is the equation of the new parabola?

\newline

y=

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y=x^{2}

is shifted up by

2

units and to the right by

3

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What is the equation of the new parabola?

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y=

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Question

y=x^{2}

is reflected across the

x

-axis and then scaled vertically by a factor of

5

\newline

What is the equation of the new parabola?

\newline

y=\square

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Question

y=x^{2}

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\newline

What is the equation of the new parabola?

\newline

y=

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