Chapter 9.9, Problem 37STP

To determine

To calculate: To find the equation that represents cubic function

Answer to Problem 37STP

  $y=5x^3$ is a cubic function.

Explanation of Solution

Given information: Functions:

  $y=5^x$

  $y=5x^2$

  $y=5x$

  $y=5x^3$

Formula Used:

Highest power of the variable in a function is referred to as degree of function.

Linear function is a function with degree 1

Quadratic function is a function with degree 2

Cubic function is a function with degree 3

Exponential function is a function with variable as exponent

Calculation:

Given functions are

  $y=5^x$

  $y=5x^2$

  $y=5x$

  $y=5x^3$

Now, consider the function $y=5^x$

Here, exponent is a variable, hence not a cubic function

Consider the function $y=5x^2$

Here, degree of function is $2$ , hence not a cubic function

Consider the function $y=5x$

Here, degree of function is $1$ , hence not a cubic function

Consider the function $y=5x^3$

Here, degree of function is $3$ , hence is a cubic function

Conclusion:

Hence, $y=5x^3$ is a cubic function.