Question

Drag the tiles tobthe correct boxes to complete the pair

Answer 1

Part 1)
`d(x)=5((1)/(3))^(x)` ----> The y-intercept is the point (0,5), graph initially decreases rapidly and then decreases slowly

Part 2)
`g(x)=((2)/(5))^(x)` ----> The y-intercept is the point (0,1), graph initially decreases rapidly and then decreases slowly

Part 3)
`h(x)=(4)^(x)` ----> The y-intercept is the point (0,1),graph initially increases slowly and then increases rapidly

Explanation:

Part 1) we have

`d(x)=5((1)/(3))^(x)`

Find the y-intercept

Remember that the y-intercept is the value of y when the value of x is equal to zero (initial value)

For x=0

Substitute

`d(0)=5((1)/(3))^(0)=5`

The y-intercept is the point (0,5)

using a graphing tool

see the attached figure N 1

The graph initially decreases rapidly and then decreases slowly

Part 2) we have

`g(x)=((2)/(5))^(x)`

Find the y-intercept

Remember that the y-intercept is the value of y when the value of x is equal to zero (initial value)

For x=0

Substitute

`g(0)=((2)/(5))^(0)=1`

The y-intercept is the point (0,1)

using a graphing tool

see the attached figure N 2

The graph initially decreases rapidly and then decreases slowly

Part 3) we have

`h(x)=(4)^(x)`

Find the y-intercept

Remember that the y-intercept is the value of y when the value of x is equal to zero (initial value)

For x=0

Substitute

`h(0)=(4)^(0)=1`

The y-intercept is the point (0,1)

using a graphing tool

see the attached figure N 3

The graph initially increases slowly and then increases rapidly