Question

Which graph shows g(x)=−5x+3+7 ?

Answer 1

The correct answer is the 4th option

Explanation:

Answer 2

Given function:
`g(x)=-5^(x+3)+7`

We need to find the correct graph in the given options.

In order to find the correct, we need to find the x-intercept.

In order to find the x-intercept, we need to put given function equal to 0 and then solve for x.

`-5^(x+3)+7=0`

Subtracting 7 from both sides, we get

`-5^(x+3) = -7`

Dividing both sides by -1, we get

`5^(x+3) =7`

Taking ln on both sides, we get

`ln(5^(x+3)) = ln(7)`

(x+3)
`ln(5) = ln(7)`

Dividing both sides, by ln(5), we get

`x+3=(ln(7))/(ln(5))`

x+3 =1.21

x= 1.21 -3

x=-1.79.

From the given options, we can see the 4th option has x-intercept at -1.79.

Therefore, 4th option is correct option.