Question

Which point is on the graph of the function

Answer 1

Answer:

  (d)  (1, 1)

Step-by-step 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:

  $\left[\begin{array}{c|cccc}x&0&1&2&3\\y&\dfrac{1}{2}&1&2&4\end{array}\right]$

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.