Chapter 6.3, Problem 44E

To determine

The graph of the function $f(x)=0.5{(4)}^x$

Answer to Problem 44E

The value of h is greater than the value of f over the rest of the interval.

Explanation of Solution

Given information:

Compare the function as given below,

  $f(x)=0.5{(4)}^x$

Over the interval as shown below,

  $x=0\text{to}x=2$

Formula used:

The divide h(x) by $\frac{1}{2}$ for every 1 unit decrease in x.

Calculation:

You know (0, 32) is on the graph of h. To find points to the right of (0, 32), multiply h(x) by $\frac{1}{2}$ for every 1 unit increase in x to find points to the left of (0, 32), divide h(x) by $\frac{1}{2}$ for every 1 unit decrease in x.

Make table of values.

  

Plot the ordered pairs.

Draw a smooth curve through the points.

  

Both functions have the same value at x = 2 but the value of h is greater than the value of f over the rest of the interval.

Conclusion:

The value of h is greater than the value of f over the rest of the interval.