Chapter 7.3, Problem 88PPS

a.

To determine

To complete the given table.

Explanation of Solution

Given:

  

Calculation:

x	-2	$-\frac{3}{2}$	-1	$-\frac{1}{2}$	0	$\frac{1}{2}$	1	$\frac{3}{2}$	2
$f(x)=4^x$	$\frac{1}{16}$	$\frac{1}{8}$	$\frac{1}{4}$	$\frac{1}{2}$	1	2	4	8	16

Conclusion:

Therefore, for different values of x, the table is completed.

b.

To determine

To sketch the graph the table from part (a)

Explanation of Solution

Given:

From subpart (a),

x	-2	$-\frac{3}{2}$	-1	$-\frac{1}{2}$	0	$\frac{1}{2}$	1	$\frac{3}{2}$	2
$f(x)=4^x$	$\frac{1}{16}$	$\frac{1}{8}$	$\frac{1}{4}$	$\frac{1}{2}$	1	2	4	8	16

Graph:

Plotting the given points in the graph,

  

Conclusion:

Therefore, the graph is plotted.

c.

To determine

To describe the shape of the graph of f(x) and find if the graph is linear.

Answer to Problem 88PPS

Curve, not linear

Explanation of Solution

Given:

Graph from subpart (b),

  

The graph of the function is a curve. The curve has no x-intercepts. The curve meets the axis at $y=1$ and the domain is all the real numbers.

Range of the function is all the positive real numbers.

The graph is not linear since it is not a straight line.

Conclusion:

Therefore, the given graph is a curve and not linear.