14. What is the graph of the function rule?
`y=\left|2x\right|-1`
Use the table to help you with graphing this function. Select a few negative numbers, a few positive numbers, and zero for your x-value.
To graph the function, we can substitute several values for x and find the corresponding values for y using the function rule y = |2x| - 1.
Let's choose the following values for x:
x = -3, -2, -1, 0, 1, 2, 3
We can then calculate the corresponding values for y:
y = |2(-3)| - 1 = 6 - 1 = 5
y = |2(-2)| - 1 = 4 - 1 = 3
y = |2(-1)| - 1 = 2 - 1 = 1
y = |2(0)| - 1 = 0 - 1 = -1
y = |2(1)| - 1 = 2 - 1 = 1
y = |2(2)| - 1 = 4 - 1 = 3
y = |2(3)| - 1 = 6 - 1 = 5
Now, we can plot these points on a graph:
(-3, 5) | |
(-2, 3) | |
(-1, 1) | |
(0, -1) | |
(1, 1) | |
(2, 3) | |
(3, 5) |____|
This graph represents the function y = |2x| - 1. The points form a "V" shape symmetric about the y-axis, with its vertex at (0, -1).