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

Answer:

The second statement is true.

Step-by-step 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

Answer:

B)

Step-by-step 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