Question

Which of the following is the parent function in the function g(x) = 4x^2 + 5x^3 - 1?

A) g(x) = 4x^2
B) g(x) = 5x^3
C) g(x) = -1
D) None of the above.

Answer 1

The parent function of g(x) = 4x^2 + 5x^3 - 1 is g(x) = 5x^3, as the cubic term has the highest degree and influences the graph's shape the most.

Step-by-step explanation:

The parent function of a function is the simplest function that maintains the shape of the graph.

For the given function g(x) = 4x^2 + 5x^3 - 1, the parent function would be the simplest form which is represented by a single term with the highest degree, that dictates the overall shape of the graph.

In this case, that would be g(x) = 5x^3, since the cubic term (x^3) has the highest degree and will dominate the shape of the graph for large values of x, both positive and negative.