Chapter 3.1, Problem 68E

Solution

a.

To identify: The curve that most closely resembles the graph of $y=f\left(x\right)$ .

The curve that most closely resembles the graph of $y=f\left(x\right)$ is $y_1$ since $f\left(x\right)$ increases less rapidly as x increases.

Given information:

The table shows the function values of $y=f\left(x\right)$ and $y=g\left(x\right)$ .

$x$	$f(x)$	$g(x)$
1.0	5.50	7.40
1.5	5.35	6.97
2.0	5.25	6.44
2.5	5.17	5.76
3.0	5.13	4.90
3.5	5.09	3.82
4.0	5.06	2.44
4.5	5.05	0.71

The graph provides three curves.

  

Explanation:

From the table, $f\left(x\right)$ increases less rapidly as x increases matches the curve $y_1$ .

b.

To identify: The curve that most closely resembles the graph of y=g(x).

The curve that most closely resembles the graph of $y=g\left(x\right)$ is $y_3$ since $g\left(x\right)$ decreases rapidly as x increases.

Given information:

The table shows the function values of $y=f\left(x\right)$ and $y=g\left(x\right)$ .

$x$	$f(x)$	$g(x)$
1.0	5.50	7.40
1.5	5.35	6.97
2.0	5.25	6.44
2.5	5.17	5.76
3.0	5.13	4.90
3.5	5.09	3.82
4.0	5.06	2.44
4.5	5.05	0.71

The graph provides three curves.

  

Explanation:

From the table, $g\left(x\right)$ decreases rapidly as x increases matches the curve $y_3$ .