Question

Given f(x) = x^2+4, does there exist an x-intercept between [-2, 3]. Why or why not. Be sure to include in your discussion the Intermediate Value Theorem

Answer 1

The x-intercepts are the values of x for which f(x) = 0.
x^2 + 4 = 0
x^2 = -4
x= ±√(-4), which are not real numbers. f(x) does not have an x-intercept.