Unit 2: Functions

Key words

• FunctionKey word · Unit 2FunctionA rule that gives one output for each allowed input.Exactly: A function assigns exactly one value in its codomain to each element of its domain.Mix-up alert: Different inputs can have the same output.See this in Key wordsClose meaning
• DomainKey word · Unit 2DomainAll the inputs you are allowed to use.Exactly: The set of input values for which a function is defined.Mix-up alert: A denominator cannot be zero; a real square root needs a nonnegative input.See this in Key wordsClose meaning
• Average rate of changeKey word · Unit 2Average rate of changeHow much the output changes per unit of input over an interval.Exactly: For $a<b$, the average rate of change of $f$ over $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$. Its units are output units per input unit.Mix-up alert: Divide the output change by the input change, in the same order.See this in Key wordsClose meaning
• CompositionKey word · Unit 2CompositionUse one function’s output as the next function’s input.Exactly: The composite function satisfies $(f\circ g)(x)=f(g(x))$. It is defined when $x$ is in the domain of $g$ and $g(x)$ is in the domain of $f$.Mix-up alert: Composition is not multiplication, and order usually matters.See this in Key wordsClose meaning
• Inverse functionKey word · Unit 2Inverse functionA rule that reverses a one-to-one function.Exactly: The inverse of a one-to-one function $f$ reverses its input-output correspondence: $f^{-1}(f(x))=x$ on the domain of $f$, and $f(f^{-1}(y))=y$ on its range.Mix-up alert: The inverse function $f^{-1}$ is not the reciprocal $\frac{1}{f(x)}$.See this in Key wordsClose meaning
• Even and odd symmetryKey word · Unit 2Even and odd symmetryA graph can match itself across the vertical axis or after a half-turn about the origin.Exactly: On a domain symmetric about zero, an even function satisfies $f(-x)=f(x)$; an odd function satisfies $f(-x)=-f(x)$.Mix-up alert: A function can be neither. The zero function is both even and odd.See this in Key wordsClose meaning