Question

Math again yay!...Ew math

Answer 1

The graph of g(x) is wider.

Explanation:

Parent function:

`f(x)=x^2`

New function:

`g(x)=\left((1)/(2)x\right)^2=(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+(1)/(4)`

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

`\implies g(x)=x^2-(1)/(4)`

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

`\implies g(x)=(1)/(4)x^2`

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

`\implies g(x)=\left((1)/(2)x\right)^2`

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