Question

Consider the function g(x) = −3f(x + 1) − 1. Choose True or False for each statement.

A. When compared to f(x) = 2x, g(x) will be reflected over the x-axis.
A True B False
B. When compared to f(x) = 2x, g(x) will have a vertical stretch of 3.
A True B False
C. When compared to f(x) = 2x, g(x) will be translated right 1 unit and up 1 unit.
A True B False

Answer 1

we are given

$g(x)=-3f(x+1)-1$

we will verify each options

option-A:

we can see that f is multiplied by -1

so, it is reflected about x-axis

so, this is TRUE

option-B:

We can see that

3 is multiplied with f

so, it is stretched vertically by 3  units

so, this is TRUE

option-C:

we are given

x+1 inside f

so, it will be  translated f(x) to left side by 1 unit

so, this is FALSE