Question

The functions f(x) and g(x) are shown on the graph.f(x) = 2xWhat is g(x)?y5f(x)X-55g(x)

Answer 1

We know that

$f(x)=2^x$

So, we can see that g(x) is f(x) reflected in the x-axis. But, it has another change which is a downward movement in 3 units.

So, we can deduce that

$g(x)=-2^x-3$

Sketch of the situation:

When you reflect f(x) in the x-axis, you obtain something like -f(x).

We can see that -f(x) intersect the y-axis in -1. But, g(x) intersect the y-axis in -4.

So, we need to move the function 3 units down. Whe we make the movement the graph will intersect the y-axis in -4 because -1-3=-4.