Question

Is `h(x)=2x^3-4x^2+5` a linear function and explain your reasoning?

Answer 1

No

Explanation:

A linear function can always be written of the form `f(x) = mx + b`, where the variable is of power `1`. Here, we have terms of power `3` and power `2`. Hence, this is not linear.

A linear function takes the form of a straight line when graphed, although this polynomial function is obviously not straight as shown in the following graph.

graph{2x^3 + 4x^2 + 5 [-10, 10, -5, 5]}

Hopefully this helps!