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.