Question
Below are the graphs of y = |x| and y = |x| - 5. How are the functions related?
The functions have the
y = x| is
shape. The y-intercept of
and the y-intercept of y = |x| - 5 is
5
The functions have the
y = x| is
shape. The y-intercept of
and the y-intercept of y = |x| - 5 is
5
Answers
GPT 3.5
The functions are related in two main ways:
1) Shape: Both functions have the same V-shape. This is because the absolute value function, |x|, always gives the distance between x and 0 (the y-axis). As x approaches positive or negative infinity, the distance between x and 0 also becomes larger, resulting in the V-shape.
2) Translation: The second function, y = |x| - 5, is the same as the first function, y = |x|, shifted downward by 5 units. This means that every point on the graph of y = |x| - 5 is 5 units below the corresponding point on the graph of y = |x|. The y-intercept of y = |x| - 5 is at y = -5, while the y-intercept of y = |x| is at y = 0.
1) Shape: Both functions have the same V-shape. This is because the absolute value function, |x|, always gives the distance between x and 0 (the y-axis). As x approaches positive or negative infinity, the distance between x and 0 also becomes larger, resulting in the V-shape.
2) Translation: The second function, y = |x| - 5, is the same as the first function, y = |x|, shifted downward by 5 units. This means that every point on the graph of y = |x| - 5 is 5 units below the corresponding point on the graph of y = |x|. The y-intercept of y = |x| - 5 is at y = -5, while the y-intercept of y = |x| is at y = 0.