Question

What are the vertex and range of y = |4x 8| − 1?

A) (0, −1); −[infinity] < y < [infinity]
B) (0, −1); −1 ≤ y < [infinity]
C) (−2, −1); −[infinity] < y < [infinity]
D) (−2, −1); −1 ≤ y < [infinity]

Answer 1

The vertex of the function y = |4x + 8| - 1 is (-2, -1) and the range is y ≥ -1, making the correct answer D) (-2, -1); − 1 ≤ y < ∞.

Step-by-step explanation:

To find the vertex and range, let's first rewrite the equation in a more familiar form. The absolute value function can be written as a piecewise function: y = 4x + 8 if 4x + 8 ≥ 0, and y = -(4x + 8) if 4x + 8 < 0. The question is about finding the vertex and the range of a transformed absolute value function, which is y = |4x + 8| − 1. There seems to be a typo in the function; it should likely be y = |4x + 8| − 1. First, to find the vertex of the absolute value function, we need to set the expression inside the absolute value to zero. Therefore, 4x + 8 = 0 which means x = -2. Substituting x = -2 into the function, we find the vertex is (-2, -1). Since absolute value functions have a minimum value where the graph turns, this function will have a lowest point at y = -1. Thus, the range of the function is y ≥ -1.

Considering these points, the correct answer is D) (-2, -1); − 1 ≤ y < ∞.