Chapter 3.2, Problem 39E

To determine

To make: a conjecture about x-intercept of $y={\left(ax+b\right)}^n$ .

Answer to Problem 39E

  $x-\text{intercept}=-\frac{b}{a}$

Explanation of Solution

Given information:

The parent function is $y=x^n$ .

  $y={\left(ax+b\right)}^n$

Calculation:

The x-intercept would have $y=0$ . So, put the value of y in the equation below and evaluate the x-intercept as follows:

  $\begin{array}{c}y={\left(ax+b\right)}^n\\ {\left(y\right)}^{\frac{1}{n}}=ax+b\\ {\left(0\right)}^{\frac{1}{n}}=ax+b\\ 0=ax+b\\ -ax=b\\ x=-\frac{b}{a}\end{array}$

Thus the x-intercept is $-\frac{b}{a}$ .