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All Flashcards
How to find given and ?
Replace in with : .
How to evaluate given and ?
First, find . Then, find .
How to decompose into two functions, and ?
Let and . Then .
How to find such that , given and ?
First find . Then solve 2x + 1 = 5
, which gives .
How to find if and ?
Substitute into : , for .
How to determine the domain of ?
Find the domain of and ensure that the range of is within the domain of .
What are the differences between and ?
: Apply first, then . | : Apply first, then . The results are generally different.
Compare vertical translation and horizontal dilation.
Vertical Translation: Shifts the graph up or down. | Horizontal Dilation: Stretches or shrinks the graph horizontally.
What is a composite function?
A function formed by applying one function to the results of another: .
What does mean?
Apply to first, then apply to the result.
What is the identity function?
The function , which returns the input unchanged.
Define function decomposition.
Breaking down a complex function into simpler component functions.
What is vertical translation in terms of function composition?
Shifting the graph of a function up or down by adding a constant, represented by .
What is horizontal dilation in terms of function composition?
Stretching or shrinking the graph of a function horizontally by multiplying the input by a constant, represented by .