Question

PLEASE HELP!

For the function f(x) = x^2, what effect will multiplying f(x) by 1/3 have on the graph?

Answer 1

For the function f ( x ) = x² we have the new function f 1 ( x ) = 1/2 x².f ( x ) = a · x²- If |a| < 1 the graph is compressed vertically by a factor of a.- If |a| > 1 the graph is stretched vertically by a factor of a.Here: a = 1/2 < 1

Answer:C. The graph will be compressed vertically.

Answer 2

Answer: The graph of f(x) would shrink vertically by
`(1)/(3)\ units`.

Explanation:

Since we have given that

`f(x)=x^2`

We need to multiply f(x) by
`(1)/(3)`

Let f(x) = y.

We have two conditions :

y=kf(x)

if k>1, then it tends to vertical stretch.

if k<1, then it tends to vertical shrink.

Since we have given that we have to multiply
`(1)/(3)` with f(x) as
`(1)/(3)<1`

so, it tends to vertical shrink, and it move closer to x-axis which make the graph flatter.

Hence, the graph of f(x) would shrink vertically by
`(1)/(3)\ units`.