Question

What is the equation of the function shown in the graph, given the equation of the parent function is f(x)=0.75^x?

Responses

g(x)=0.75x+3
g begin argument x end argument equals 0.75 begin power x end power plus 3

g(x)=0.75x−1
g begin argument x end argument equals 0.75 begin power x end power minus 1

g(x)=0.75x−2
g begin argument x end argument equals 0.75 begin power x end power minus 2

g(x)=0.75x+2

Answer 1

The function in the graph is g(x) = 0.75ˣ + 2, the correct option is the last one.

What is the equation of the function shown in the graph?

We can see that we have a translation of the function:

f(x) = 0.75ˣ

First, we can see that when x = 0, the function passes through (0, 3), then if we have a vertical translation of N units we can write:

g(x) = 0.75ˣ + N

Now we evaluate in the point above:

3 = 0.75⁰ + N

3 = 1 + N

3 - 1 = N

2 = N

Then:

g(x) = 0.75ˣ + 2