Question

The x-values in the table for f(x) were multiplied by -1 to create the table for g(x). What is the relationship between the graphs of the two functions?

f(x)

x y

-2 -31

-1 0

1 2

2 33


g(x)

x y

2 -31

1 0

-1 2

-2 33




A.

They are reflections of each other over the line x = y.


B.

The graphs are not related.


C.

They are reflections of each other across the x-axis.


D.

They are reflections of each other across the y-axis.

Answer 1

The graph of g(x) will be the reflection of f(x) in the y axis.

Explanation:

Because the corresponding x values in f(x) and g(x) are symmetrical about the y axis.

Answer 2

D. They are reflections of each other across the y-axis.

Explanation:

F(x) becomes g(x) the only difference is that x becomes negative x

(x,y) → (-x,y) reflection over the y-axis

If we had had

(x,y) → (x,-y) reflection over the x-axis

(x,y) → (y,x) reflection over the line x=y