Nonlinear Functions

Question

Which of the following is an example of a graph in the xy-plane of a function with exactly one real zero?

A. A linear function with a slope of zero

B. A quadratic function with exactly one x-intercept

C. A quadratic function with x-intercepts

D. A fourth degree polynomial with no x-intercepts

Answer 1

A real zero on a graph is where it crosses the x axis, i.e., an x intercept

A. A linear function with a slope of zero

A horizontal line that does not cross the x axis so no real zeros

B. A quadratic function with exactly one x-intercept

An x intercept is where it crosses the x axis, so one real zero

C. A quadratic function with x-intercepts

If more than 1 x intercept, then more than one real zero.

D. A fourth degree polynomial with no x-intercepts

No x intercepts means no real zeros.

Answer 2

What is the definition of "a zero"?