Chapter 3.2, Problem 33PPS

To determine

To find: The zero of a given function $f\left(x\right)=\frac{3}{4}-\frac{2}{5}x$ by graphing.

Answer to Problem 33PPS

The required zero of the given function $f\left(x\right)=\frac{3}{4}-\frac{2}{5}x$ is $\frac{15}{8}$ .

Explanation of Solution

Given information:

The given function $f\left(x\right)=\frac{3}{4}-\frac{2}{5}x$

Calculation:

Make a table to graph the function.

x	$f\left(x\right)=\frac{3}{4}-\frac{2}{5}x$	$f\left(x\right)$	$\left(x,f\left(x\right)\right)$
-1	$f\left(-1\right)=\frac{3}{4}-\frac{2}{5}\left(-1\right)$	$\frac{23}{20}$	$\left(-1,\frac{23}{20}\right)$
0	$f\left(0\right)=\frac{3}{4}-\frac{2}{5}\left(0\right)$	$\frac{3}{4}$	$\left(0,\frac{3}{4}\right)$
2	$f\left(2\right)=\frac{3}{4}-\frac{2}{5}\left(2\right)$	$-\frac{1}{20}$	$\left(2,-\frac{1}{20}\right)$

The graph intersects the x-axis at $\frac{15}{8}$ or 1.875. So, the zero is $\frac{15}{8}$ .