Chapter 9.6, Problem 42HP

To determine

Wheather the graph of $y=a{b}^x,wherea\ne 0,b\ge 1andb\ne 1$ sometimes, always, or never has an x-intercepts

Answer to Problem 42HP

We see that the graph $y=a{b}^x$ never has an x-intercept

Explanation of Solution

Given information:

Graph of $y=a{b}^x,wherea\ne 0,b\ge 1andb\ne 1$

Concept Used:

Exponential function: have the form of $y=a{b}^x\text{and}a\ge 1$ and the rate of change increases very slow at first and then rapidly increased.

In order to find the graph we take the value of a and b in equation $y=a{b}^x$ as below:

  

Thus, we see that the graph $y=a{b}^x$ never has an x-intercept