Chapter 3.2, Problem 43PPS

To determine

To find: the zero given functions by graphing and verify answer algebraically.

Answer to Problem 43PPS

The option D is correct answer.

Explanation of Solution

Given information:

Given function,

  $f\left(x\right)=-\frac{8}{3}x+3$

Calculation:

Consider the given function,

  $f\left(x\right)=-\frac{8}{3}x+3$

Now, the tables are,

$x$	$f\left(x\right)$
0	3
0.125	2.666667
0.25	2.333333
0.375	2
0.5	1.666667
0.625	1.333333
0.75	1
0.875	0.666667
1	0.333333
1.125	0
1.25	$-0.33333$
1.375	$-0.66667$
1.5	$-1$
1.625	$-1.33333$
1.75	$-1.66667$
1.875	$-2$
2	$-2.33333$

Graph:

  

In the graph above, plot $f(x)$ vs. $x$ . It is clear from the graph that $f\left(x\right)=0$ , when $x=1.125$ .

Detailed explanation algebraically is shown below.

Now, find out the value of $x$ corresponding to $f\left(x\right)=0$

Now, solve the function,

  $\begin{array}{c}f(x)=-\frac{8}{3}x+3\\ 0=-\frac{8}{3}x+3\\ \frac{8}{3}x=3\\ x=\frac{3\times 3}{8}\\ x=1.125\end{array}$

Thus, its verified.