Question

Math again yay!...Ew math

Answer 1

Answer:

The graph of g(x) is wider.

Step-by-step explanation:

Parent function:

$f(x)=x^2$

New function:

$g(x)=\left(\dfrac{1}{2}x\right)^2=\dfrac{1}{4}x^2$

Transformations:

For a > 0

$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

$f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}$

$\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of}\:a\\ & \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a\\\end{aligned}$

$\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of} \: a\\& \textsf{If }a > 1 \textsf{ it is compressed by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of}\: a\\\end{aligned}$

If the parent function is shifted ¹/₄ unit up:

$\implies g(x)=x^2+\dfrac{1}{4}$

If the parent function is shifted ¹/₄ unit down:

$\implies g(x)=x^2-\dfrac{1}{4}$

If the parent function is compressed vertically by a factor of ¹/₄:

$\implies g(x)=\dfrac{1}{4}x^2$

If the parent function is stretched horizontally by a factor of ¹/₂:

$\implies g(x)=\left(\dfrac{1}{2}x\right)^2$

Therefore, a vertical compression and a horizontal stretch mean that the graph of g(x) is wider.