I need to make tables of values for both horizontal and vertical stretching, but I wasn't in class and missed the lesson. I don't really understand how to get the values; at first I figured you'd get the value of y by just pluging in whatever value of x you're given to y=f(x), but this doesn't seem to work. My book shows completely different answers, but doesn't explain how to get them.
I'm given a table of values for y=f(x) with (-4,0), (-2,4), (0,-4), (2,4), (4,0). Then, I am to find the y values for y=2f(x) and for y=1/2f(x) and for y=f(2x) and y=F(1/2x).
I'm guessing that if there's an actual number inside the parenthesis, it's a horizontal stretch, but I still can't figure out how to actually do it.
Please help me.
I'd be happy to help you understand how to create tables of values for horizontal and vertical stretching!
To start, let's look at the basic function y = f(x) and the given table of values for y = f(x): (-4,0), (-2,4), (0,-4), (2,4), (4,0).
To find the values for y = 2f(x), you need to multiply each y-value in the original table by 2. For example, the first point (-4,0) becomes (-4, 2*0 = 0), and the second point (-2,4) becomes (-2, 2*4 = 8). Continuing this process, you can create a new table of values for y = 2f(x).
To find the values for y = 1/2f(x), you need to multiply each y-value in the original table by 1/2. For example, the first point (-4,0) becomes (-4, 1/2*0 = 0), and the second point (-2,4) becomes (-2, 1/2*4 = 2). Continue this process to create a new table of values for y = 1/2f(x).
Next, let's look at the functions y = f(2x) and y = f(1/2x).
To find the values for y = f(2x), you need to substitute the values of x from the original table into 2x. For example, the first point (-4,0) becomes (-4/2 = -2, 0), and the second point (-2,4) becomes (-2/2 = -1, 4). Continue this process to create a new table of values for y = f(2x).
To find the values for y = f(1/2x), you need to substitute the values of x from the original table into 1/2x. For example, the first point (-4,0) becomes (-4/2 = -2, 0), and the second point (-2,4) becomes (-2/2 = -1, 4). Continue this process to create a new table of values for y = f(1/2x).
In summary, to create tables of values for horizontal and vertical stretching, follow these steps:
1. For vertical stretching:
- Multiply the y-values of the original table by the stretch factor. In your case, it's y = 2f(x) and y = 1/2f(x).
2. For horizontal stretching:
- Substitute the values of x from the original table into the expression inside the parentheses. In your case, it's y = f(2x) and y = f(1/2x).
Remember to carry out the calculations correctly and carefully to get the accurate values for the new tables.