Question

The graph of a function increases twice as much over each subsequent equally sized interval. Which of the following could be the parent function of the graphed function?

y=2^x
y=x^2
y=the absolute value of 2x
y=sqr root of x

Answer 1

y = 2^x

By increasing over each interval "twice as much" as the previous one, you should get points like (1, 2), (2, 4), and (3, 8). At x = 2, y = 4, which is twice as much as the value at x = 1, where y = 2 (2 x 2 = 4). This pattern is observable in the other following points.

If you make a chart of the values plotted by y = 2^x, they correlate, proving the answer.

x = 1, y = 2
x = 2, y = 4
x = 3, y = 8
x = 4, y = 16
x = 5, y = 32
...