I am struggling with how to start this problem.
The following points are on the graph of: y=f(x)
Use theorem to identify the corresponding points on the transformed functions.
y = 2f(x-3)-2
point will be in the y twice as high but -2 lower, and each x will be shifted right 3
I forgot to add the points on the graph of y=f(x):
(-5,0),(-2,2),(0,0),(2,-4) and (4,0)
y = 2f(x-3)-2
To identify the corresponding points on the transformed function, it is important to understand what each part of the equation represents.
First, let's break down the given equation: y = 2f(x-3)-2
1. The number "2" in front of f(x-3) represents vertical stretching or compression. If the value is greater than 1, it stretches the graph vertically, while if it is between 0 and 1, it compresses the graph vertically. In this case, it stretches the graph vertically by a factor of 2.
2. The expression (x-3) inside f(x) represents horizontal shifting. Substituting x with (x-3) will shift the graph horizontally to the right by 3 units.
3. Finally, the "-2" at the end of the equation represents the vertical shifting. It moves the graph down by 2 units.
To find the corresponding points, follow these steps:
Step 1: Take the given points on the original graph, which we will call (x, y).
Step 2: Substitute (x-3) into the equation instead of x to find the new x-coordinate for the transformed function.
Step 3: Multiply the corresponding y-coordinate by 2 and then subtract 2 from the result.
The new coordinates for the transformed function will be (x', y').
Let's go through an example:
Suppose one of the points on the original graph is (5, 7).
Step 1: The original point is (5, 7).
Step 2: Substitute (x-3) into the equation instead of x:
x' = (5-3) = 2
Step 3: Multiply the corresponding y-coordinate by 2 and subtract 2:
y' = 2 * 7 - 2 = 12
Therefore, the corresponding point on the transformed function is (2, 12).
Repeat this process for all the points on the original graph to find the corresponding points on the transformed function.