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What kind of transformation converts the graph of $f(x) = 9|x - 2| - 2$ into the graph of $g(x) = 9|x + 1| - 2$ ? $\newline$ Choices: $\newline$ (A) translation $3$ units left $\newline$ (B) translation $3$ units up $\newline$ (C) translation $3$ units right $\newline$ (D) translation $3$ units down

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Describe function transformations

Full solution

Q. What kind of transformation converts the graph of

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

into the graph of

g(x) = 9|x + 1| - 2

?

\newline

Choices:

\newline

(A) translation

3

units left

\newline

(B) translation

3

units up

\newline

(C) translation

3

units right

\newline

(D) translation

3

units down

Identify Vertex of $f(x)$ : Identify the vertex of the function $f(x) = 9|x - 2| - 2$ . The vertex of the absolute value function $f(x) = 9|x - h| - k$ is at the point $(h, k)$ . For $f(x) = 9|x - 2| - 2$ , $h = 2$ and $k = -2$ . Vertex of $f(x)$ : $(2, -2)$
Identify Vertex of $g(x)$ : Identify the vertex of the function $g(x) = 9|x + 1| - 2$ . Similarly, for $g(x) = 9|x - h| - k$ , $h = -1$ and $k = -2$ . Vertex of $g(x)$ : $(-1, -2)$
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 vertex of $f(x)$ is at $(2, -2)$ and the vertex of $g(x)$ is at $(-1, -2)$ . Horizontal shift: $2 - (-1) = 3$ units to the left.
Determine Vertical Shift: Determine the 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 $-2$ , there is no vertical shift. Vertical shift: $-2 - (-2) = 0$ units.

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{]}

Posted 3 months ago

Question

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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Question

What does the transformation

f(x) \mapsto f(4x)

do to the graph of

f(x)

\newline

\newline

[A] stretches it vertically

\newline

[B] stretches it horizontally

\newline

[C]shrinks it horizontally

\newline

[D]shrinks it vertically

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Question

g(x)

g(x)

is the translation

9

f(x) = 10x + 8

\newline

\newline

g(x) = 10x - 82

\newline

g(x) = 10x + 98

\newline

g(x) = 10x - 1

\newline

g(x) = 10x + 17

Posted 3 months ago

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}

\newline

\text{[D]translation 10 units right}

Posted 2 months ago

Question

y=x^{2}

is scaled vertically by a factor of

7

. What is the equation of the new parabola?

\newline

y=

Posted 4 months ago

Question

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=

Posted 4 months ago

Question

y=x^{2}

is shifted up by

2

units and to the right by

3

\newline

What is the equation of the new parabola?

\newline

y=

Posted 2 months ago

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

Posted 2 months ago

Question

y=x^{2}

is scaled vertically by a factor of

\frac{1}{10}

\newline

What is the equation of the new parabola?

\newline

y=

Posted 3 months ago