Question

Which of the following statements are true about the function represented by the graph below?

The function is negative over the interval (-infinity, infinity)
The function is negative over the interval (-infinity, 7]
The function is positive over the interval (-infinity, -4]
The function is negative over the interval [-1, infinity)
The function is positive over the interval [-2, infinity)

Answer 1

The true statements about the function represented by the graph are:

The function is negative over the interval (-infinity, 7].

The function is negative over the interval [-1, infinity).

Based on the graph and the given information about the function, we can determine the following:

Statement 1: "The function is negative over the interval (-infinity, infinity)"

False. The function is positive over the interval (-4, 7).

Statement 2: "The function is negative over the interval (-infinity, 7]"

True. The function is negative for all values less than or equal to 7.

Statement 3: "The function is positive over the interval (-infinity, -4]"

False. The function is negative for all values less than or equal to -4.

Statement 4: "The function is negative over the interval [-1, infinity)"

True. The function is negative for all values greater than or equal to -1.

Statement 5: "The function is positive over the interval [-2, infinity)"

False. The function is negative for some values within the interval [-2, infinity), specifically between the points (0, -3) and (7, 0).

Therefore, the true statements about the function represented by the graph are:

The function is negative over the interval (-infinity, 7].

The function is negative over the interval [-1, infinity).