Question

In the function y=1/2x^2 , what effect does the number 1/2 have on the graph, as compared to the graph of the function y=x^2 ?

A. It shrinks the graph vertically to 1/2 its original height.
B. It stretches the graph vertically by a factor of 2.
C. It stretches the graph horizontally by a factor of 2.
D. It shrinks the graph horizontally to 1/2 its original width.
In the function y=1/2x^2 , what effect does the number 1/2 have on the graph, as compared to the graph of the function y=x^2 ?

A. It shrinks the graph vertically to 1/2 its original height.
B. It stretches the graph vertically by a factor of 2.
C. It stretches the graph horizontally by a factor of 2.
D. It shrinks the graph horizontally to 1/2 its original width.

Answer 1

D isn't the correct answer. It's "It shrinks the graph vertically to 1/2 its original height."

Explanation:

I'm not sure why though this is right because I graphed it, and I don't see how that could be the right answer.

Answer 2

Option A - It shrinks the graph vertically to 1/2 its original height.

Explanation:

Given : In the function
`y=(1)/(2) x^2`

To find : What effect does the number
`(1)/(2)` have on the graph, as compared to the graph of the function
`y=x^2` ?

Solution :

The parent function is
`y=x^2`

We have given that
`(1)/(2)` number is multiply to the parent function.

When the unit is multiply to the function gives you vertical stretch or compression

i.e, f(x)→ bf(x), o<b<1 then the function is vertically compressed.

`y=(1)/(2) x^2` As
`0<(1)/(2)<1` means there is vertical compression or shrinks.

Therefore, Option A is correct.

It shrinks the graph vertically to 1/2 its original height.