Chapter 3.2, Problem 1BGP

To determine

To find:

Zero of the function, $f\left(x\right)=-1.25x+3$ graphically as well as algebraically.

Answer to Problem 1BGP

Zero of the function is $x=2.4$ .

Explanation of Solution

Given information:

A function, $f\left(x\right)=-1.25x+3$ .

Conceptused:

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 $f(x)=0$ and solve it for x.

Calculation:

To find zero algebraically, plug in $f(x)=0$ in given equation and solve it for x,

  $\begin{array}{l}0=-1.25x+3\\ \Rightarrow 1.25x=3\\ \Rightarrow x=\frac{3}{1.25}=2.4\end{array}$

To graph it, its two points to be calculated as:

x	$f\left(x\right)=-1.25x+3$	$(x,f\left(x\right))$
2.4	$=-1.25(2.4)+3=-3+3=0$	$(2.4,0)$
0	$=-1.25(0)+3=0+3=3$	$(0,3)$

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

  

And this graph shows that its zero is at $x=2.4$ as the line intersects x axis at this point.

Conclusion:

In both methods, the zero of the function is $x=2.4$ .