I'm having trouble getting through these types of problems:
Can someone tell me how to approach this?
The point (8, -4) is on the graph of y=f(x). Find the corresponding point on the graph of
g(x)=3f(1/2x)+11
Any assistance would be greatly appreciated!
-Brett
You know that f(8) = -4
So, if you want f(x/2), you need x/2 = 8, so x = 16
g(16) = 3f(8)+11 = 3(-4)+11 = -1
So the point (16,-1) is on the graph of g(x)
I was setting everything up backwards. Thank you for the clarification. These questions ACTUALLY make sense now!
Feels good, don't it?
To find the corresponding point on the graph of g(x) given a point on the graph of f(x), you need to perform the following steps:
Step 1: Start with the given point (8, -4) on the graph of f(x).
Step 2: Substitute x = 8 and y = -4 into the equation g(x) = 3f(1/2x) + 11.
Step 3: Calculate the value of 1/2x: 1/2 * 8 = 4.
Step 4: Substitute the value obtained in the previous step (4) into f(1/2x): f(4).
Step 5: Find the value of f(4) on the graph of f(x).
Step 6: Substitute the values obtained in steps 4 and 5 into the equation g(x) = 3f(1/2x) + 11 to find the corresponding point on the graph of g(x).
Let's now go through the steps using the given point (8, -4):
Step 1: Start with the point (8, -4).
Step 2: Substitute x = 8 and y = -4 into the equation g(x) = 3f(1/2x) + 11:
g(8) = 3f(1/2 * 8) + 11.
Step 3: Calculate 1/2x:
1/2 * 8 = 4.
Step 4: Substitute the value obtained in the previous step (4) into f(1/2x):
f(4).
Step 5: Find the value of f(4) on the graph of f(x). This step requires information about the function f(x) itself, which you haven't provided. You need to know the equation or a given table of values for f(x) to evaluate f(4).
Step 6: Substitute the values obtained in steps 4 and 5 into the equation g(x) = 3f(1/2x) + 11 to find the corresponding point on the graph of g(x). This step can only be completed once you have the value of f(4).
Please provide the equation or more information about the function f(x) to proceed further and find the corresponding point on the graph of g(x).