Chapter 3.2, Problem 40PPS

To determine

To find: Zero of the function $f\left(x\right)=-2x+4$graphically as well as algebraically.

Answer to Problem 40PPS

Zero of the function is $x=2$ .

Explanation of Solution

Given information: A function $f\left(x\right)=-2x+4$ .

Concept used: Graphically, the zero of a function is/are the value(s) of its independent variable on x axis, where its graph intersects the x axis. And to get its zero algebraically, put $f\left(x\right)=0$ and solve it for x.

Calculation: On plug in $f\left(x\right)=0$ in given equation and on solving it for x,

  $\begin{array}{l} 0=-2x+4\\ \Rightarrow 2x=4\\ \Rightarrow x=\frac{4}{2}=2\end{array}$

And to graph it, its two points to be calculated are,

x	$f\left(x\right)=-2x+4$	$(x,f\left(x\right))$
0	$=2(0)+4=4$	$(0,4)$
2	$=-2(2)+4=-4+4=0$	$(2,0)$

On plotting these points in XY plane, its graph is shown as:

  

This graph shows that its zero is $x=2$as the line intersects x axis at this point.

Conclusion: In both methods, the zero of the function is $x=2$ .