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 true statement about the function f(x) = -x² - 4x + 5 is that:

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

What is the domain and range for the function of y = f(x)?

The domain of a function is the set of given values of input for which the function is valid and true.

The range is the dependent variable of a given set of values for which the function is defined.

• The domain of the function: f(x) = -x² - 4x + 5 are all real number from -∞ to +∞

For a parabola ax² + bx + c  with the vertex $\mathbf{(x_v,y_v)}$

• If a < 0, then the range is f(x) ≤ $\mathbf{y_v}$

• If a > 0, then the range f(x) ≥  $\mathbf{y_v}$

• Here; a = -1,

The vertex for an up-down facing parabola for a function y = ax² + bx + c is:

$\mathbf{x_v = -\dfrac{b}{2a}}$

Thus,

• vertex $\mathbf{(x_v,y_v)}$ = (-2, 9)

Range: f(x) ≤ 9

Therefore, we can conclude that the range of the function is all real numbers less than or equal to 9.

Learn more about the domain and range of a function here:

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