Question

Which points are on the graph of f(x)=(13) x? Select each correct answer.

A (3, 27)
B (−2, 9)
C (0, 1)
D (−1, −13)]

Answer 1

D

Explanation:

The function is f(x)=13x. To find the point on the graph, we substitute a corrdinate pair (x,f(x)) into the equation. When we substitute D (-1,-13), we find:

x=-1 f(x)=-13

-13=13(-1)

-13=-13.

(-1,-13) is on the graph.

Answer 2

B and C

Explanation:

We are given that a function

`f(x)=((1)/(3))^x`

A.(3,27)

Substitute x=3

`f(3)=((1)/(3))^3=(1)/(27)`

`(3,27)\\eq (3,1/27)`

Hence, it is not true.

B.(-2,9)

Substitute x=-2

`f(-2)=((1)/(3))^(-2)=3^2=9`

By using identity
`(1)/(a^x)=a^(-x)`

Therefore, point(-2,9) lies on the given graph.

Hence, it is true.

C.(0,1)

Substitute x=0

`f(0)=((1)/(3))^0=1`

By using
`a^0=1`

Hence, it is true.

D.(-1,-13)

Substitute x=-1

`f(-1)=((1)/(3))^(-1)=3`

Hence, the point (-1,-13) does not lie on the graph.