Composition of Functions with Graphs and Tables

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•
Mathematics
•
9th - 11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a function composition?
Back
Function composition is the process of applying one function to the results of another function. If you have two functions, f(x) and g(x), the composition is denoted as (f ∘ g)(x) = f(g(x)).
2.
FLASHCARD QUESTION
Front
How do you evaluate h(f(-2)) if h(x) = 2x and f(x) = x + 2?
Back
First, find f(-2): f(-2) = -2 + 2 = 0. Then, find h(0): h(0) = 2(0) = 0.
3.
FLASHCARD QUESTION
Front
What is the notation for function composition?
Back
The notation for function composition is (f ∘ g)(x), which means f(g(x)).
4.
FLASHCARD QUESTION
Front
If f(x) = 3x + 10, what is f(2)?
Back
f(2) = 3(2) + 10 = 6 + 10 = 16.
5.
FLASHCARD QUESTION
Front
What is the result of f(g(5)) if f(x) = 3x + 10 and g(x) = x - 2?
Back
g(5) = 5 - 2 = 3. Then, f(g(5)) = f(3) = 3(3) + 10 = 9 + 10 = 19.
6.
FLASHCARD QUESTION
Front
How do you find h(f(g(-2))) if h(x) = -3x, f(x) = x^2 - 2, and g(x) = x + 9?
Back
First, find g(-2): g(-2) = -2 + 9 = 7. Then, find f(7): f(7) = 7^2 - 2 = 49 - 2 = 47. Finally, find h(47): h(47) = -3(47) = -141.
7.
FLASHCARD QUESTION
Front
What is the composition of functions f(x) = x^2 and g(x) = 1/x^2?
Back
The composition (f ∘ g)(x) = f(g(x)) = f(1/x^2) = (1/x^2)^2 = 1/x^4.
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