Question

Multiple Choice

Describe how the graphs of y = |x| and y = |x| – 15 are related.
A. The graphs have the same shape. The y-intercept of y = |x| is 0, and the x-intercept of the second graph is –15.
B.
The graphs have the same y-intercept. The second graph is steeper than y = |x|.

C. The two graphs are the same.
D. The graphs have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second graph is –15.

Answer 1

D is correct

Explanation:

A graph of that sort will make a perfectly mirrored "V" shape, and with no offset, the bottom point will be on the y axis. This means that the first equation will intercept the y axis at zero, the second will intercept the y-axis at -15.

"A" may seem correct also, as the second graph will intercept the x-axis at -15, but it is not complete, as it will intercept that axis at +15 as well.

Answer 2

The correct answer is D. The graphs have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second graph is –15.

The graph of y = |x| represents the absolute value function, which is symmetric about the y-axis and passes through the origin (0, 0). It has a V-shape with the vertex at the origin.

When you subtract 15 from the absolute value function to get y = |x| – 15, it shifts the entire graph downward by 15 units. This means that the new y-intercept is at y = -15 (when x = 0).

Despite the vertical shift, the basic shape of the graph remains the same, with the characteristic V-shape. The graphs have the same shape, but the second graph is shifted downward.

Option D correctly captures this relationship by stating that the graphs have the same shape, and the y-intercept of y = |x| is 0, while the y-intercept of the second graph is –15.