Chapter Functions

y = f(x + c), shift the graph of y = f(x) to the ____ c units

left

Let f be a function. f is ______ if f(-x) = -f(x) for all x in the domain of f.

odd

y = f(x - c), shift the graph of y = f(x) to the ____ c units

right

To graph y = cf(x). If 0 < c < 1, ______ the graph of y = f(x) vertically by a factor c.

shrink

To graph y = f(cx). If c > 1, ____ the graph of y = f(x) horiontal by a factor of 1/c

shrink

To graph y = cf(x). If c > 1, _____ the graph of y = f(x) _____ by a factor c.

stretch

To graph y = f(cx). If 0 < c < 1, ____ the graph of y = f(x) horiontal by a factor of 1/c

stretch

y = f(x) + c, shift the graph of y = f(x) ____ c units

upward

To graph y = -f(x), reflect the graph of y = f(x) in the _____-axis.

x

To graph y = f(-x), reflect the graph of y = f(x) in the _____-axis.

y

f is ________ on an interval I if f(x1) > f(x2) whenever x1 < x2 in I.

increasing

Let f be a one-to-one function with domain A and range B. Then its ____ function f_inverse has domain B and range A and is defined by f_inverse (y) = x <> f(x) = y for any y in B

inverse

f is ________ on an interval I if f(x1) < f(x2) whenever x1 < x2 in I.

decreasing

Recall that the _____ of a function is the set of all inputs for the function.

domain

y = f(x) - c, shift the graph of y = f(x) ____ c units

downward

Let f be a function. f is ______ if f(-x) = f(x) for all x in the domain of f.

even

A _______ f is a rule that assigns to each element x in a set A exactly one element, called f1x2, in a set B.

function

A function is one-to-one if and only if no ______line intersects its graph more than once

horizontal