Chapter 3.1, Problem 1E

Solution

To decide: if the given function is an exponential function.

No, it is not an exponential function.

Given information:

The given function is:

  $y=x^8$

Definition Used:

The general form of an exponential function f ( x ) is

  $f\left(x\right)=a\cdot b^x$   ..... (1)

Where $a\ne 0$, b is a positive real number called the base of the function and $b\ne 1$ .

Here, x is a variable and is called the exponent.

Explanation:

From the above definition of an exponential function, it is clear that an exponential function has a constant base and a variable exponent.

Now, consider the given function $y=x^8$ .

In this function, the base is x which is a variable and the exponent is 8, which is constant.

So, this function doesn’t satisfy the above definition.

Hence, it is not an exponential function.