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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. A1. independent dependent. Q2.

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chapter 2 review

Chapter 2 Review

Concepts and Vocabulary

slide2
Q1.

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

slide3
A1.

independent

dependent

slide4
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.

slide5
A2.

vertical

slide6
Q3.

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

slide7
A3.

range

slide8
Q4.

True or False:

Every relation is a function.

slide9
A4.

False

slide10
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).

slide11
A5.

True

slide12
Q6.

True or False:

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

slide13
A6.

True

slide14
Q7.

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

slide15
A7.

slope

y-intercept

slide16
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.

slide17
A8.

True

slide18
Q9.

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

slide19
A9.

slope

slide20
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).

slide21
A10.

increasing

slide22
Q11.

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

slide23
A11.

even

slide24
Q12.

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

slide25
A12.

odd

slide26
Q13.

True or False:

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

slide27
A13.

false

slide28
Q14.

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

slide29
A14.

less

slide30
Q15.

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

slide31
A15.

piecewise

slide32
Q16.

True or False:

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

slide33
A16.

true

slide34
Q17.

True or False:

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

slide35
A17.

false

slide36
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 _?_.

slide37
A18.

horizontal

right

slide38
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).

slide40
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 _?_.

slide41
A20.

stretch

3

slide42
Q21.

True or False:

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

slide43
A21.

true

slide44
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.

slide45
A22.

false

slide46
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.

slide47
A23.

true

slide48
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 _?_.

slide49
A24.

[0,5]

slide50
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 _?_.

slide51
A25.

f

g

slide52
Q26.

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

slide53
A26.

g(f(x))

slide54
Q27.

True or False:

f(g(x)) = f(x)· g(x)

slide55
A27.

false

slide56
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.

slide57
A28.

true

slide58
Q29.

True or False:

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

slide59
A29.

false

slide60
Q30.

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

slide61
A30.

Work problems!

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