Question

Which point is on the graph of the function

f(x) = 1/2(2)^x
0 (0, 1)
0 (0, 2)
O (1,1/2)
O (1,1)

Answer 1

(d) (1, 1)

Explanation:

You can plot the points on a graph, or you can evaluate the function.

f(0) = 1/2(2^0) = 1/2

f(1) = 1/2(2^1) = 1

The point (1, 1) is on the graph.

_____

Additional comment

The function is of the form ...

f(x) = a(b^x)

In this form, 'a' is the "initial value," the y-intercept, the value of f(0). The value 'b' multiplies the function value each time x increases by 1. This means you can easily create a table of points on the graph:

`\left[\begin{array}ccccx&0&1&2&3\\y&(1)/(2)&1&2&4\end{array}\right]`

Notice each y-value is 2× the previous one when x increases by 1. The graph is plotted as a smooth curve through these points. A graphing calculator is a handy tool for showing the curve.