Chapter 7.5, Problem 44HP

To determine

To find if the functions are increasing, decreasing, positive or negative, relative maxima and minima, symmetry and end behavior.

Answer to Problem 44HP

The functions are increasing, positive, has no maxima and minima and no symmetry.

Explanation of Solution

Given:

Function:

  $f(x)=a{b}^x+c$

  $g(x)=ax+c$

Concept used:

Maxima is the highest value of a function and minima is the lowest point of a function.

Symmetry is the condition wherein the axes cut the curve equally.

The end behavior of a function is the behavior of the graph at the ends of the x- axis.

Calculation for graph:

Consider $f(x)=8x^3-14x^2+18x-9$

Values of x	$f(x)=3\times 2^x+1$	$g(x)=3x+1$
-5	1.09	-14
-4	1.18	-11
-3	1.37	-8
-2	1.75	-5
-1	2.5	-2
0	4	1
1	7	4
2	13	7
3	25	10
4	49	13

By taking different values of x , the graph can be plotted.

Graph:

  

Interpretation:

From the graph the red line represents $f(x)$ and the green line represents $g(x)$

The y- intercept of $f(x)$ is 4 and the y- intercept of $g(x)$ is 1. As x increases, both $f(x)$ and $g(x)$ increases. The function $f(x)$ has positive values for all real numbers but $g(x)$ does not have only positive values. Both the functions do not have maxima or minima and neither has symmetry.

Conclusion:

Therefore, the function is increasing, positive, has no maxima and minima and no symmetry.