Describe how the graphs of y = absolute value of x,and y = absolute value of X -15 are related.
1- Them graphs have the same shape. The y intercept of y = absolute x is 0, and them x intercept of the 2nd graph is -15.
2-m The graphs have the same y intercept. The second graph is steeper than y = absolute X.
3-The graphs are the same.
4-The graphs have the same shape. The y- intercept of y =absolute X is 0, and the y intercept of the second graph is-15.
Thank you -- A Grandfather trying to help his Grandson.
If you mean |x|-15
then as usual, the graph is shifted down 15 units.
It's a lot easier to figure out what you mean if you just use proper notation.
If you meant |x-15| then none of the choices is correct.
The correct answer is:
1- The graphs have the same shape. The y-intercept of y = absolute x is 0, and the x-intercept of the second graph is -15.
The correct answer is:
2- The graphs have the same y-intercept. The second graph is steeper than y = absolute X.
To understand why this is the correct answer, let's explain the relationship between the two graphs.
The graph of y = |x| represents the absolute value of x, which means that it takes the input value (x) and returns its positive value. This graph resembles a V-shape, with the vertex (lowest point) at the origin (0, 0). It has a y-intercept at (0, 0), which is where it intersects the y-axis.
On the other hand, the graph of y = |x - 15| represents the absolute value of (x - 15). This means that the input value (x) gets subtracted by 15 first, and then its absolute value is taken. This graph also has a V-shape, but it is shifted horizontally by 15 units to the right compared to y = |x|. Its y-intercept is at (0, 15), which means it intersects the y-axis at a height of 15.
Since both graphs have V-shapes and share the same y-intercept (at a height of 0), we can conclude that choices 1 and 3 are incorrect.
The correct answer is choice 2 - the graphs have the same y-intercept. However, the second graph is steeper than y = |x|. This means that the steepness or slope of the graph of y = |x - 15| is greater than the graph of y = |x|.
Therefore, the second graph rises more rapidly as we move away from the y-intercept, indicating a steeper slope.