Question

Select all functions that have a y-intercept of (0,5).

f(x)=7(b)^x-2
f(x)=-3(b)^x-5
f(x)=5(b)^x-1
f(x)=-5(b)^x+10
f(x)=2(b)^x+5

Answer 1

`f(x)=7(b)^(x)-2`

`f(x)=-5(b)^(x)+10`

Explanation:

we know that

The y-intercept is the value of y when the value of x is equal to zero

Verify each case

case 1) we have

`f(x)=7(b)^(x)-2`

so

For x=0

`f(0)=7(b)^(0)-2`

`f(0)=7(1)-2=5`

therefore

The function has a y-intercept of (0,5)

case 2) we have

`f(x)=3(b)^(x)-5`

so

For x=0

`f(0)=3(b)^(0)-5`

`f(0)=3(1)-5=-2`

therefore

The function does not have a y-intercept of (0,5)

case 3) we have

`f(x)=5(b)^(x)-1`

so

For x=0

`f(0)=5(b)^(0)-1`

`f(0)=5(1)-1=4`

therefore

The function does not have a y-intercept of (0,5)

case 4) we have

`f(x)=-5(b)^(x)+10`

so

For x=0

`f(0)=-5(b)^(0)+10`

`f(0)=-5(1)+10=5`

therefore

The function has a y-intercept of (0,5)

case 5) we have

`f(x)=2(b)^(x)+5`

so

For x=0

`f(0)=2(b)^(0)+5`

`f(0)=2(1)+5=7`

therefore

The function does not have a y-intercept of (0,5)