If the point P is on the graph of a function f, find thecorresponding point on the graph of a given function: P(3,-2), y=2f(x-4)+1
x-4 is 3
so x is 7
f(x-4) = -2
so y = 2(-2) + 1 = -4+1 = -3
Well, P(3,-2) sounds like a famous pirate code. It seems like we're on an exciting adventure here. Now let's calculate the corresponding point on the graph of our given function y=2f(x-4)+1.
To find this point, let's first focus on the x-coordinate of point P. It's 3. Now, according to the given function, we need to adjust it by subtracting 4: (x-4). I hope x doesn't drop anchor with surprise because we're just getting started, matey!
By substituting this adjusted value into our given function, we get:
y=2f(3-4)+1
Now, let's calculate f(3-4):
f(-1)
Awesome! We're getting closer to our treasure. Now, substituting this into the original equation, we have:
y=2*f(-1)+1
And there you have it, folks! We've reached our destination. The corresponding point on the graph of the given function is:
(-1, 2*f(-1)+1)
Keep laughing and adventuring, matey!
To find the corresponding point on the graph of the given function, we need to substitute the x-coordinate of point P into the given function and then calculate the y-coordinate.
Given: P(3, -2) and y = 2f(x-4) + 1
1. Substitute the x-coordinate of point P into the given function:
y = 2f(3-4) + 1
2. Simplify the expression inside the parentheses:
y = 2f(-1) + 1
3. Since point P is on the graph of function f, we know that f(3) = -2. Substitute this value into the equation:
y = 2(-2) + 1
4. Simplify the expression:
y = -4 + 1
5. Final calculation:
y = -3
Therefore, the corresponding point on the graph of the given function is (-1, -3).
To find the corresponding point on the graph of the given function, we can use the given point P(3, -2) and the equation y = 2f(x - 4) + 1. Here's how you can determine the corresponding point:
Step 1: Start with the coordinates of the given point P, which are (3, -2).
Step 2: Substitute the x-coordinate of point P into the equation y = 2f(x - 4) + 1.
Substituting x = 3, the equation becomes:
y = 2f(3 - 4) + 1
Simplifying, we get:
y = 2f(-1) + 1
Step 3: Now, we need to determine the value of f(-1), which corresponds to the y-coordinate of the new point on the graph of the given function.
Step 4: If the graph of function f is given or you have a specific equation for f, substitute x = -1 into the function f(x) to find f(-1).
Since the information about function f is not provided, you need to have knowledge about f or more information to determine its value at x = -1.
Once you have the value of f(-1), substitute it back into the equation y = 2f(-1) + 1 to obtain the corresponding y-coordinate of the point on the graph of the given function.
Note: Without information about function f, it is not possible to find the corresponding point on the graph of the given function.