Chapter 1.3, Problem 32E

To determine

To state: a linear function that is not zero and another linear function that has infinitely many zeros.

Answer to Problem 32E

  $\begin{array}{l}f\left(x\right)=1\\ f\left(x\right)=0\end{array}$

Explanation of Solution

Given information:

Linear function that is not a zero.

Linear function with infinite zeros.

Calculation:

For a linear function to have no zero, the two lines should never intersect. The function $f\left(x\right)=1$ is parallel to x-axis and the lines don not intersect with each other. Thus, the function $f\left(x\right)=1$ is a no zero linear function.

The zeros of function the points where the function is equal to zero, and the line function $f\left(x\right)=0$ has infinitely many zeros.