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What does the transformation $f(x) \mapsto f(x - 4)$ do to the graph of $f(x)$ ? $\newline$ Choices: $\newline$ (A) $\text{translates it } 4 \text{ units right}$ $\newline$ (B) $\text{translates it } 4 \text{ units down}$ $\newline$ (C) $\text{translates it } 4 \text{ units left}$ $\newline$ (D) $\text{translates it } 4 \text{ units up}$

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Function transformation rules

Full solution

Q. What does the transformation

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

do to the graph of

f(x)

?

\newline

Choices:

\newline

(A)

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

\newline

(B)

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

\newline

(C)

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

\newline

(D)

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

Given Transformation: We are given the transformation $f(x) \mapsto f(x - 4)$ . We need to determine how this transformation affects the graph of the original function $f(x)$ .
Recognition of Horizontal Shift: Recognize that the transformation involves the input variable $x$ . The transformation $f(x) \mapsto f(x - 4)$ indicates a horizontal shift, as it changes the $x$ -value at which a particular $y$ -value of the function is obtained.
Direction of Horizontal Shift: Determine the direction of the horizontal shift. In the transformation $f(x) \mapsto f(x - 4)$ , the $x$ -value is being reduced by $4$ before being input into the function. This means that every point on the graph of $f(x)$ will be shifted to the right by $4$ units to compensate for this reduction.
Confirmation of Vertical Shift: Confirm that the transformation does not involve any vertical shift, as there is no addition or subtraction outside the function $f(x)$ . Therefore, there is no translation up or down.

More problems from Function transformation rules

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 2 months ago

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

Posted 1 month ago

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 2 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 1 month 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 1 month 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

Question

Find the value of

x

in these diagrams.

\newline

\newline

Posted 12 hours ago