SAT II Math I : Transformations
Study concepts, example questions & explanations for SAT II Math I
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Example Questions
Example Question #11 : Transformation
What would 
When a function is reflected over the y-axis, 
becomes
which is simplifed as
Example Question #1 : Transformation
Let f(x) = x3 – 2x2 + x +4. If g(x) is obtained by reflecting f(x) across the y-axis, then which of the following is equal to g(x)?
–x3 – 2x2 – x + 4
x3 + 2x2 + x + 4
–x3 + 2x2 – x + 4
–x3 – 2x2 – x – 4
x3 – 2x2 – x + 4
–x3 – 2x2 – x + 4
In order to reflect a function across the y-axis, all of the x-coordinates of every point on that function must be multiplied by negative one. However, the y-values of each point on the function will not change. Thus, we can represent the reflection of f(x) across the y-axis as f(-x). The figure below shows a generic function (not f(x) given in the problem) that has been reflected across the y-axis, in order to offer a better visual understanding.
Therefore, g(x) = f(–x).
f(x) = x3 – 2x2 + x – 4
g(x) = f(–x) = (–x)3 – 2(–x)2 + (–x) + 4
g(x) = (–1)3x3 –2(–1)2x2 – x + 4
g(x) = –x3 –2x2 –x + 4.
The answer is –x3 –2x2 –x + 4.
Example Question #4 : Transformation
What is the period of the function?
2π
3π
π
1
4π
4π
The period is the time it takes for the graph to complete one cycle.
In this particular case we have a sine curve that starts at 0 and completes one cycle when it reaches 
Therefore, the period is
Example Question #471 : Advanced Geometry
Assume we have a triangle, 
If 
When we reflect a point across the line, 
The correct answer is the following:
The other answer choices are incorrect because we only use the negatives of the coordinate points if we are flipping across either the x- or y-axis.
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