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### Chapter 2 Review

Concepts and Vocabulary

Q1.

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

Q2.

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.

A2.

vertical

Q3.

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

A3.

range

A4.

False

Q5.

True or False:

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

A5.

True

Q6.

True or False:

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

A6.

True

Q7.

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

Q8.

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.

A8.

True

Q9.

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

A9.

slope

Q10.

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).

A10.

increasing

Q11.

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

A11.

even

Q12.

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

A12.

odd

A13.

false

Q14.

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

A14.

less

Q15.

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

A15.

piecewise

A16.

true

Q17.

True or False:

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

A17.

false

Q18.

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 _?_.

Q19.

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).

A19.

y

Q20.

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 _?_.

Q21.

True or False:

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

A21.

true

Q22.

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.

A22.

false

Q23.

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.

A23.

true

Q24.

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 _?_.

A24.

[0,5]

Q25.

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

Q26.

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

A26.

g(f(x))

A27.

false

Q28.

True or False:

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

A28.

true

Q29.

True or False:

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

A29.

false

Q30.

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

A30.

Work problems!

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