Question

What are the vertex and range of y = |x 2| − 3?

A) (−2, −3); −[infinity] < y < [infinity]
B) (−2, −3); −3 ≤ y < [infinity]
C) (0, −1); −[infinity] < y < [infinity]
D) (0, −1); −3 ≤ y < [infinity]

Answer 1

The vertex of the function y = |x + 2| - 3 is (-2, -3) and the range is -3 ≤ y < ∞, making the correct answer B) (-2, -3); -3 ≤ y < ∞.

Step-by-step explanation:

The given function is y = |x + 2| − 3. To find the vertex of the absolute value function, we set the expression inside the absolute value to zero. Thus, we have x + 2 = 0, which gives us x = −2. Substituting x = −2 into the function gives us the y-coordinate of the vertex: y = |−2 + 2| − 3 = 0 − 3 = −3. Therefore, the vertex of the function is (−2, −3).

Now, let's consider the range of the function. Since the lowest value of y occurs at the vertex (because the absolute value function opens upwards), and the y-value of the vertex is −3, the function does not go below y = −3. Therefore, the range of the function is −3 ≤ y < ∞. Hence, the correct answer is B) (−2, −3); −3 ≤ y < ∞.