Chapter 7.6, Problem 64HP

To determine

To determine the point which lies on the graph of given function

Answer to Problem 64HP

  $(0,1)$

Explanation of Solution

Given:

  $f(x)=b^x$ where $b\ne 0$

The given function is an exponential function and these functions are either monotonically increasing or decreasing. And they cut the y -axis at (0,1).

Calculation:

We have,

  $f(x)=b^x$ where $b\ne 0$

Now,putting $x=0$ in the given function

  $y=f(0)=b^0=1$

Which means that the value of function at $x=0$ is independent of b and will always be equal to $y=1$ .

Conclusion:

Hence,the point which lies on the graph of every function of the given form will be $(0,1)$ .