Question

The graphs below have the same shape. The equation of the blue graph is f(x) = 2x. Which of these is the equation of the red graph, g(x)?

Answer 1

The main thing you want to ask yourself is "What is the difference between the two graphs?"

As we can see, the graphs look identical in every way except that g(x) is lower than f(x).

This means that the graph is shifted down a certain amount.

If we look at the y-intercepts of the two functions, we see that f(x) has a y-intercept of 1, and g(x) has a y-intercept of -1.

This means that f(x) is two units lower than g(x).

The y-intercept of a function can be changed by adding or subtracting a number to the original function (in this case 2^{x}).

Because the graph f(x) is 2 lower than the graph of g(x), we can find g(x) by subtracting 2 from f(x).

Therefore, g(x) = 2^{x} - 2.