Question

\The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.

Answer 1

The range of the function is all real numbers less than or equal to 9.

Explanation:

Domain is the set of all x values that result in a real and well defined value for a function

Range is the set of all output values for that function for the given domain

Plotting the function shows that the x values can range from -∞ to +∞. In other words the domain is - ∞ < x < ∞

So the first and second choices are out

Looking at the output values for the function we see that the maximum value of f(x) is 9. There is no bound on the lower limit, So the range of this function is f(x) ≤ 9 which corresponds to the last statement:

The range of the function is all real numbers less than or equal to 9.