Chapter 2 Vocabulary

-f(x), f(-x)

A reflection in the x-axis of y=f(x) is represented by h(x)=_____, while a reflection in the y-axis of y=f(x) is represented by h(x)=_____.

domain, range, function

A relation that assigns to each element x from a set of inputs, or _____, exactly one element y in a set of outputs, or _____, is called a _____.

average rate of change, secant

The _____ _____ _____ between any two points (x1, f(x1)) and (x2, f(x2)) is the slope of the line through the two points, and this line is called the _____ line.

vertical line test

The _____ _____ _____ is used to determine whether the graph of an equation is a function of y in terms of x.

zeros

The _____ of a function f are the values of x in which f(x)=0.

composition

The _____ of the function f with g is (fog)(x)=f(g(x)).

point-slope

The _____-_____ form of the equation of a line with slope m passing through (x1, y1) is y-y1=m(x-x1).

reciprocal function

f(x)= 1/x

greatest integer function

f(x)=((x)) (BRACKETS)

absolute value function

f(x)=(x) (BRACKETS)

linear function

f(x)=ax+b

constant function

f(x)=c

square root function

f(x)=square root (x)

identity function

f(x)=x

squaring function

f(x)=x^2

cubic function

f(x)=x^3

decreasing

A function f is _____ on an interval when, for any x1, and x2 in the interval, x1<x2 implies f(x1)>f(x2).

one-to-one

A function f is _____ when each value of the dependent variable corresponds to exactly one value of the independent variable.

odd

A function f is _____ when, for each x in the domain of f, f(-x)=-f(x).

maximum

A function value f(a) is a relative _____ of f when there exists an interval (x1,x2) containing a such that x1<x<x2 implies f(a) > or = to f(x).

horizontal

A graphical test for the existence of an inverse function of f is called the _____ Line Test.

vertical stretch, vertical shrink

A nonrigid transformation of y=f(x) represented by g(x)=cf(x) is a _____ _____ when c>1 and a _____ _____ when 0<c<1.

general

Every line has an equation that can be written in _____ form.

slope

For a line, the ratio of the change in y to the change in x is called the _____ of the line.

independent, dependent

For an equation that represents y as a function of x, the set of all values taken on by the _____ variable x is the domain, and the set of all values taken on by the _____ variable y is the range.

rigid

Horizontal shifts, vertical shifts, and reflections are called _____ transformations.

inverse

If the composite functions f(g(x)) and g(f(x)) both equal x, then the functions g is the _____ function of f.

implied domain

If the domain of the function f is not given, then the set of values of the independent variable for which the expression is defined is called the _____ _____.

difference quotient

In calculus, one of the basic definitions is that of the _____ _____ given by f(x+h)-f(x)/h, h is NOT=0.

linear

The constant function and the identity function are two special types of _____ functions.

range, domain

The domain of f is the _____ of f^-1, and the _____ of f^-1 is the range of f.

y=x

The graphs of f and f^-1 are reflections of each other in the line _____.

f^-1

The inverse function of f is denoted by _____.

linear extrapolation

The prediction method _____ _____ is the method used to estimate a point on a line when the point does not lie between the given points.

linear

The simplest mathematical model for relating two variables is the _____ equation in two.

addition, subtraction, multiplication, division

Two functions f and g can be combined by the arithmetic operations of _____, _____, _____, and _____ to create new functions.

parralel

Two lines are _____ if and only if their slopes are equal.

perpendicular

Two lines are _____ if and only if their slopes are negative reciprocals of each other.

rate

When the x-axis and y-axis have different units of measure, the slope can be interpreted as a _____.