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

Sep 3, 2017

No

#### Explanation:

A linear function can always be written of the form $f \left(x\right) = m x + b$, 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!