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 _____.
