Unit 1
Function notation, domain and range, and the transformations that move any graph. Learned once, this unit applies to every family that follows.
Lesson 1.1
A function assigns exactly one output to each permitted input. Evaluate by replacing every occurrence of the variable. A real-valued square root requires a nonnegative radicand, and a denominator cannot be zero. Range describes actual outputs and may be narrower than all real numbers.
Lesson 1.2
Transformations act on inputs and outputs in different ways. Subtracting h inside the function moves a graph right by h. Adding k outside moves it up by k. Multiplying outputs scales vertically and a negative output factor reflects across the x-axis.
Lesson 1.3
Composition applies one function and then the other, so order matters. The output of the inner function must lie in the outer function domain. An inverse reverses a one-to-one relationship; finding a formula involves swapping input and output roles and solving.
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