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 [-1, infinity), which corresponds to answer option d.

Step-by-step explanation:

To find the vertex and range of the function y = |4x + 8| − 1, we first determine the vertex of the absolute value function. The equation inside the absolute value, 4x + 8 = 0, gives us the x-coordinate of the vertex when we solve for x. Therefore, x = −2. The y-coordinate of the vertex is obtained by substituting x back into the function, resulting in y = −1. This makes the vertex (−2, −1).

Given that the absolute value function opens upwards and has been shifted downwards by 1 unit, the minimum value of y is −1 and the function extends infinitely upwards. Hence, the range of the function is [−1, infinity). The correct answer is option d: vertex at (−2, −1) and range is [−1, infinity).