Section 4.6: Nonlinear Functions

Nonlinear functions are functions whose graphs are not straight lines. Examples include quadratic, cubic, exponential, and absolute value functions.

Example 1

Graph the quadratic function \( f(x) = x^2 - 4 \).

The graph is a parabola opening upwards with vertex at (0, -4).

Determine if \( g(x) = 2^x \) is linear or nonlinear.

Since the graph of \( 2^x \) is curved, it is a nonlinear function.

Graph \( h(x) = -x^2 + 3x + 2 \).
Determine whether \( k(x) = x^3 \) is linear or nonlinear.
Graph \( p(x) = |x| \) and identify its shape.
Explain why \( f(x) = 5x + 1 \) is linear but \( f(x) = x^2 + 5x + 1 \) is nonlinear.
Identify the type of function for \( g(x) = 3^x \) and \( g(x) = \sqrt{x} \).