Below are the functions of y = |x| and y = |x| – 5. How are the functions related? Two absolute value graphs are shown. The first passes through the points left parenthesis negative 5 comma 5 right parenthesis, left parenthesis 0 comma 0 right parenthesis, and left parenthesis 5 comma 5 right parenthesis. The second passes through points left parenthesis negative 5 comma 0 right parenthesis, left parenthesis 0 comma negative 5 right parenthesis, and left parenthesis 5 comma 0 right parenthesis. (1 point) Responses The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is 5. The functions have the same shape. The y -intercept of y = | x | is 0, and the y -intercept of the second function is 5. The functions have the same y-intercept. The second function is steeper than y = |x|. The functions have the same y -intercept. The second function is steeper than y = | x |. The two functions are the same. The two functions are the same. The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is –5.

Question

Below are the functions of y = |x| and y = |x| – 5. How are the functions related? Two absolute value graphs are shown. The first passes through the points left parenthesis negative 5 comma 5 right parenthesis, left parenthesis 0 comma 0 right parenthesis, and left parenthesis 5 comma 5 right parenthesis. The second passes through points left parenthesis negative 5 comma 0 right parenthesis, left parenthesis 0 comma negative 5 right parenthesis, and left parenthesis 5 comma 0 right parenthesis. (1 point) Responses The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is 5. The functions have the same shape. The y -intercept of y = | x | is 0, and the y -intercept of the second function is 5. The functions have the same y-intercept. The second function is steeper than y = |x|. The functions have the same y -intercept. The second function is steeper than y = | x |. The two functions are the same. The two functions are the same. The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is –5.

Answer 1

The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is 5.

Answer 2

The correct response is: The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is 5.

Answer 3

To determine how the functions y = |x| and y = |x| – 5 are related, we need to analyze their characteristics based on the given information.

First, let's consider the function y = |x|. This function represents the absolute value of x. It is a V-shaped graph and passes through the points (-5,5), (0,0), and (5,5). The y-intercept of this function is 0.

Next, let's examine the function y = |x| – 5. This is another absolute value function, but it is obtained by shifting the graph of y = |x| downward by 5 units. It passes through the points (-5,0), (0,-5), and (5,0). The y-intercept of this function is 5.

From this analysis, we can conclude that the functions have the same shape, which is a V-shape. However, they differ in their y-intercepts. The y-intercept of y = |x| is 0, while the y-intercept of y = |x| – 5 is 5.

Therefore, the correct response would be: "The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is 5."