Question

Which statements about the graph of the function f(x) = -x² - 4x + 2 are true? Select three options.

The domain is x ≤-2.
The range is {yly ≤ 6}
The function is increasing over the interval (-∞, -2).
The function is decreasing over the interval (-4,00).
The function has a positive y-intercept

Answer 1

• The range is {y l y ≤ 6}.
• The function is increasing over the interval (-∞, -2).
• The function has a positive y-intercept.

Explanation:

The attached graph shows the graph opens downward, so the vertex at (-2, 6) is a maximum. The y-intercept is the constant, +2.

Range

The range is the vertical extent of the function. Its upper limit is the maximum value of the function (6), and its lower limit is negative infinity.

The range is {y l y ≤ 6}.

Increasing

The graph opens downward, so it is increasing to the left of its maximum value, and decreasing to the right of its maximum. The x-coordinate of the maximum (-2) defines the upper limit of the increasing interval.

The function is increasing over the interval (-∞, -2).

Y-intercept

The y-intercept of the graph is where it crosses the y-axis. The value of x is zero there, so the value of the function is the value of its constant, +2.

The function has a positive y-intercept.