Point (-6,12) is on the graph of y=f(x). Find a point on the transformed function y=-2f(x-1)
a)(-7,-24)
b)(-5,-6)
c)(-5,-24)
d)(-7,-6)
In general, you can translate the graph of a function to the right (+x direction) by h if you transform the function from f(x) to f(x-h).
A reflection about the x-axis is done by transforming from f(x) to -f(x).
A stretching by a factor of k in the y-direction requires a transformation of f(x) to k.f(x). For example, a stretching of twice in the y-direction would require a transformaton from f(x) to 2f(x).
The given transformation is a combination of all of the three transformations above.
Send in your answer for a check if you wish.
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To find a point on the transformed function y = -2f(x-1), we can start with the given point (-6,12) on the original function y = f(x).
Step 1: Substitute the x-coordinate of the given point (-6,12) into the transformation equation, x - 1.
(-6 - 1) = -7
Step 2: Substitute the result from Step 1 into the original function y = f(x).
y = f(-7)
Step 3: Multiply the result from Step 2 by -2 to apply the transformation.
y = -2f(-7)
Step 4: Find the value of y by evaluating the transformed function.
Option a) (-7,-24): This point does not satisfy the transformed function.
Option b) (-5,-6): This point does not satisfy the transformed function.
Option c) (-5,-24): This point does satisfy the transformed function.
Option d) (-7,-6): This point does not satisfy the transformed function.
Therefore, the correct answer is c)(-5,-24).
To find a point on the transformed function y = -2f(x-1), we need to apply the given transformation to the original point (-6,12) on the graph of y = f(x).
Let's start with the original point (-6,12) and apply the transformation:
1. First, we shift the x-coordinate 1 unit to the right.
The new x-coordinate is -6 + 1 = -5.
2. Then, we substitute the new x-coordinate into the original function f(x) to find the y-coordinate.
So, we evaluate f(-5) to find the y-coordinate.
Since the original function f(x) is not given, we can't directly calculate f(-5). However, since the transformed function is y = -2f(x-1), we know that the y-coordinate will be twice the value of f(-5) and have the opposite sign.
If we assume that f(-5) = 6 (which is not given in the question), then multiplying it by -2 gives -2 * 6 = -12.
Therefore, the point on the transformed function is (-5, -12).
Now, let's check which answer choice matches the point (-5, -12):
a) (-7, -24)
b) (-5, -6)
c) (-5, -24)
d) (-7, -6)
The correct answer is (b) (-5, -6) because it matches the point (-5, -12) that we calculated.
It's important to note that without the original function f(x) or more information, we can't definitively determine the exact point on the transformed function. This solution illustrates the process of transforming a given point on a function based on the given transformation.