Question

The function g(x) is a transformation of the parent function f(x). Decide how f(x) was transformed to make g(x).

A) Horizontal or vertical reflection.
B) Horizontal or vertical stretch.
C) Horizontal or vertical shift
D) Reflection across the line y=x

Answer 1

B) Horizontal or vertical stretch.

Explanation:

The other user was correct when I took the quiz, and here's why:

(-2, 1/9)--->(-2, 1/81)

(-1, 1/3)--->(-1, 1/27)

(2, 9)--->(2, 1)

(3, 27)--->(3, 3)

(4, 81)--->(4, 9)

The “x” or the input value is not changing at all.

The “y” or output value is being multiplied by “1/9.”

When a function is being multiplied by a coefficient, it is stretched vertically or horizontally. For that reason, the answer is B!

Note: Make sure to look at the values on your tables, because if they are different from the image given here, then the correct answer will be different too. This answer only applies to this image of values!

Answer 2

B) Horizontal or vertical stretch.

Explanation:

Given : The function g(x) is a transformation of the parent function f(x).

To Find: Decide how f(x) was transformed to make g(x).

Solution:

Vertical Stretch :
`g(x)=a f(x)`

Horizontal Stretch :
`g(x)=f(a x)`

Vertical reflection:
`g(x)=-f(x)`

Horizontal reflection:
`g(x)=f(-x)`

Vertical shift:
`g(x)=f(x)+k`

Horizontal shift:
`g(x)=f(x-h)`

The reflection of the point (x,y) across the line y = x is the point (y, x).

By the given tables we can see that

`g(x)=(1)/(9) f(x)`

Condition of Vertical stretch applies here .

So, Option B is correct.

B) Horizontal or vertical stretch.