Functions and Their Graphs Flashcards

Question 1

What is a function?

Accepted Answer

A relation that assigns each input $x$ in the domain to exactly one output $f(x)$ in the range.

Question 2

How do you test whether a function is even?

Accepted Answer

Even if $f(-x)=f(x)$ for all $x$ in the domain; the graph is symmetric about the $y$-axis.

Question 3

What vertical and horizontal stretches/compressions are produced by $g(x)=a\,f(x)$ and $g(x)=f(bx)$?

Accepted Answer

Vertical: $g(x)=a f(x)$ multiplies all $y$-values by $a$ (stretch if $|a|>1$, compression if $0<|a|<1$; reflect over $x$-axis if $a<0$). Horizontal: $g(x)=f(bx)$ scales $x$ by factor $\frac{1}{|b|}$ (compression if $|b|>1$, stretch if $0<|b|<1$; reflect over $y$-axis if $b<0$).

Functions and Their Graphs Flashcards

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