Question

The graph of the function f(x) = –(x + 3)(x – 1) is shown below.

On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 1, 4), and goes through (1, 0).


Which statement about the function is true?


A) The function is positive for all real values of x where x < –1.


B) The function is negative for all real values of x where x < –3 and where x > 1.


C) The function is positive for all real values of x where x > 0.


D) The function is negative for all real values of x where x < –3 or x > –1.

Answer 1

The second statement is true.

Explanation:

"The function is positive" means the graph is above the x-axis. The y values are positive.

"The function is negative" means the graph is below the x-axis. The y values are negative.

The first statement is false because there are values of x less than -1 where the graph is below the x-axis (example: x = -4).

The second statement says the graph is below the x-axis for values of x in two places: x to the left of -3, x to the right of 1. That's true.

The third statement is false because there are values of x to the right of 0 where the graph is below the x-axis.

The fourth statement is false. It is correct that the graph is below the x-axis for all x < -3, but for x > -1, the graph lies partly above and partly below the x-axis.

Answer 2

B)

Explanation:

f(x) = –(x + 3)(x – 1)

A) Untrue: the function is positive when -3 < x < 1 only

B) True : the function is negative when x < -3 and x > 1

C) Untrue: the function is positive when -3 < x < 1 only

D) Untrue: the function is negative when x < -3 and x > 1