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Chapter 2 Review

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Chapter 2 Review

Concepts and Vocabulary

If a function is defined by the equation y = f(x), then x is called the _?_ variable and y is the _?_ variable.

independent

dependent

A set of points in the xy-plane is the graph of a function if and only if every _?_ line intersects the graph in at most one point.

vertical

The set of all images of the elements in the domain of a function is called the _?_.

range

True or False:

Every relation is a function.

False

True or False:

The y-intercept of the graph of the function y = f(x), whose domain is all real numbers, is f(0).

True

True or False:

The independent variable is sometimes referred to as the argument of the function.

True

For the graph of the linear function f(x) = mx + b, m is the _?_ and b is the _?_.

slope

y-intercept

True or False:

The correlation coefficient is a measure of the strength of a linear relation between two variables and must lie between -1 and 1, inclusive.

True

The average rate of change of a function equals the _?_ of the secant line.

slope

A function f is _?_ on an open interval if for any choice of x1 and x2 in the interval, with x1<x2, we have f(x1) < f(x2).

increasing

An _?_ function f is one for which f(-x) = f(x) for every x in the domain of f.

even

An _?_ function f is one for which f(-x) = -f(x) for every x in the domain of f.

odd

True or False:

Even functions have graphs that are symmetric with respect to the origin.

false

The graph of f(x) = mx + b is decreasing if m is _?_ than zero.

less

When functions are defined by more than one equation, they are called _?_ functions.

piecewise

True or False:

The cube function is odd and is increasing on the interval (- ∞, ∞).

true

True or False:

The domain and range of the reciprocal function are the set of all real numbers.

false

Given f(x), then the graph of y = f(x – 2) may be obtained by a(n) _?_ shift of the graph of f a distance of 2 units to the _?_.

horizontal

right

Given f(x), then the graph of y = f(-x) may be obtained by a reflection about the _?_-axis of the graph of the function y = f(x).

y

Given f(x), then the graph of y = 3f(x) may be obtained by a vertical _?_ of the graph of f by a factor of _?_.

stretch

3

True or False:

The graph of y = - f(x) is the reflection about the x-axis of the graph of y = f(x).

true

True or False:

To obtain the graph of y = f(x+2) – 3, shift the graph of y = f(x) horizontally to the right 2 units and vertically down 3 units.

false

True or False:

To obtain the graph of y = f(4x), horizontally compress the graph of y = f(x) by a factor of 4. That is, divide each x-coordinate on the graph of y = f(x) by 4.

true

If the domain of f is all real numbers in the interval [0,7], and the domain of g is all real numbers in the interval [-2,5], then the domain of f + g is all real numbers in the interval _?_.

[0,5]

The domain of f/g consists of all real numbers x for which g(x) _?_ 0 that are in the domains of both _?_ and _?_.

≠

f

g

If f(x) = x + 1 and g(x) = x³, then _?_ = (x + 1)³ .

g(f(x))

True or False:

f(g(x)) = f(x)· g(x)

false

True or False:

The domain of (f· g)(x) consists of the numbers x that are in the domains of both f and g.

true

True or False:

The domain of the composite function (f ◦ g)(x) is the same as the domain of g(x).

false

What is the best way to study for a Math test?

Work problems!