Transformations and Function Compositions Checkpoint

Transformations and Function Compositions Checkpoint

Assessment

Flashcard

Mathematics

11th Grade

Practice Problem

Hard

CCSS
HSF-BF.A.1C, 8.F.B.4, 7.EE.A.1

+3

Standards-aligned

Created by

Wayground Content

FREE Resource

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a function composition?

Back

A function composition is the application of one function to the results of another function. It is denoted as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

2.

FLASHCARD QUESTION

Front

How do you find the composition of two functions f and g?

Back

To find the composition f ∘ g, substitute g(x) into f. For example, if f(x) = 2x and g(x) = x + 3, then f ∘ g(x) = f(g(x)) = f(x + 3) = 2(x + 3) = 2x + 6.

Tags

CCSS.HSF-BF.A.1C

3.

FLASHCARD QUESTION

Front

What is the difference between f(g(x)) and g(f(x))?

Back

f(g(x)) applies g first and then f to the result, while g(f(x)) applies f first and then g. The order of operations matters and can lead to different results.

Tags

CCSS.HSF-BF.A.1C

4.

FLASHCARD QUESTION

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

5.

FLASHCARD QUESTION

Front

How do you determine the composition function f ∘ g from their graphs?

Back

To determine f ∘ g from the graphs, find the output of g for a given input x, then use that output as the input for f. The resulting value is f(g(x)).

Tags

CCSS.HSF-BF.A.1C

6.

FLASHCARD QUESTION

Front

What is the significance of the order of operations in function composition?

Back

The order of operations in function composition affects the outcome. For example, applying g first may yield a different result than applying f first.

Tags

CCSS.HSF-BF.A.1C

7.

FLASHCARD QUESTION

Front

What is the graphical interpretation of shifting a function?

Back

Shifting a function vertically or horizontally involves adding or subtracting a constant to/from the function's input or output, respectively. For example, f(x - 4) shifts the graph of f left by 4 units.

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