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If you apply the changes below to the linear parent function, [tex]f(x) = x[/tex], what is the equation of the new function?

- Vertically stretch by a factor of 4.
- Flip over the [tex]x[/tex]-axis.

A. [tex]g(x) = \frac{1}{4} x - 1[/tex]
B. [tex]g(x) = \frac{1}{4} x[/tex]
C. [tex]g(x) = -\frac{1}{4} x[/tex]
D. [tex]g(x) = -4 x[/tex]

Sagot :

GinnyAnswer
To determine the equation of the new function resulting from the given transformations to the linear parent function [tex]\( f(x) = x \)[/tex], we will follow these steps:

Step 1: Vertically stretch by a factor of 4

A vertical stretch of a function by a factor [tex]\( k \)[/tex] involves multiplying the function by [tex]\( k \)[/tex].

For the linear parent function [tex]\( f(x) = x \)[/tex], stretching it vertically by a factor of 4 results in:

[tex]\[ f(x) = 4x \][/tex]

Step 2: Flip over the [tex]\( x \)[/tex]-axis

Flipping a function over the [tex]\( x \)[/tex]-axis involves multiplying the function by [tex]\(-1\)[/tex].

Applying this transformation to our equation from Step 1, [tex]\( f(x) = 4x \)[/tex]:

[tex]\[ f(x) = -4x \][/tex]

Therefore, the correct equation of the new function after applying the given transformations is [tex]\( g(x) = -4x \)[/tex].

Hence, the correct answer is:

D. [tex]\( g(x) = -4x \)[/tex]
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