Question

If f(x) has a y-intercept at 3 and x-intercepts at 2 and −4, and if

g(x) = −2f(−2x), what are the intercepts of g(x)?

Answer 1

Explanation:

The y-intercept of g(x) is 3 * -2 = -6.

To find the x-intercepts of g(x), we need to find the values of x that make g(x) equal to 0. Since g(x) = -2f(-2x), this means we need to find the values of x that make f(-2x) equal to 0. Therefore, we can find the x-intercepts of g(x) by solving the equation f(-2x) = 0 for x.

Since the x-intercepts of f(x) are at 2 and -4, this means that the equation f(x) = 0 has solutions at x = 2 and x = -4. Substituting these values into the equation f(-2x) = 0, we get:

f(-2(2)) = 0

f(-4) = 0

and

f(-2(-4)) = 0

f(8) = 0

Therefore, the x-intercepts of g(x) are at x = -2 and x = 4. These are the only intercepts of g(x) that we can determine for certain.