Question: which exponential function has an x-intercept?
Explanation:
Let the function:
[tex]f(x)=100^{x\text{ -5 }}\text{ - 1}[/tex]
An x-intercept or zero of the function is when y= f(x)=0. In this case, notice that this occurs when x=5, since:
[tex]f(5)=100^{5\text{ -5 }}\text{ - 1= 100}^0\text{ - 1 = 1-1 =0}[/tex]
thus, this function must cross the x-axis at the point x= 5. On the other hand, this function has a horizontal asymptote at y=-1, so the range of this function would be all y > -1. This fact further evidences that this function crosses the x-axis.
Answer: we can conclude that the correct answer is:
[tex]f(x)=100^{x\text{ -5 }}\text{ - 1}[/tex]
