M3 Mid Exam Function Transformations Compositions Inverses

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Mathematics
•
11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a transformation in the context of functions?
Back
A transformation refers to the alteration of a function's graph through shifts, stretches, compressions, or reflections.
2.
FLASHCARD QUESTION
Front
Describe the effect of the transformation p(x) = f(x + 3).
Back
This transformation shifts the graph of f(x) left by 3 units.
3.
FLASHCARD QUESTION
Front
What does a reflection over the x-axis do to a function?
Back
It inverts the y-values of the function, changing f(x) to -f(x).
4.
FLASHCARD QUESTION
Front
What is the effect of a vertical stretch on a function?
Back
A vertical stretch multiplies the function's output by a factor greater than 1, making the graph taller.
5.
FLASHCARD QUESTION
Front
How do you represent a reflection over the y-axis in a function?
Back
To reflect a function over the y-axis, replace x with -x in the function's equation.
6.
FLASHCARD QUESTION
Front
What is the composition of functions?
Back
The composition of functions involves applying one function to the result of another, denoted as (f ∘ g)(x) = f(g(x)).
7.
FLASHCARD QUESTION
Front
If f(x) = 1/x and g(x) = 3x + 2, what is f(g(x))?
Back
f(g(x)) = \frac{1}{3x + 2}.
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