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Chapter 2 Review Concepts and Vocabulary. Q1. If a function is defined by the equation y = f(x),...

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Chapter 2 Review Chapter 2 Review Concepts and Vocabulary Concepts and Vocabulary
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Page 1: 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.

Chapter 2 ReviewChapter 2 Review

Concepts and VocabularyConcepts and Vocabulary

Page 2: 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.

Q1.Q1.

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

Page 3: 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.A1.

independentindependent

dependentdependent

Page 4: 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.Q2.

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

Page 5: 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.

A2.A2.

verticalvertical

Page 6: 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.

Q3.Q3.

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

Page 7: 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.

A3.A3.

rangerange

Page 8: 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.

Q4.Q4.

True or False:True or False:

Every relation is a function.Every relation is a function.

Page 9: 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.

A4.A4.

FalseFalse

Page 10: 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.

Q5.Q5.

True or False:True or False:

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

Page 11: 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.

A5.A5.

True True

Page 12: 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.

Q6.Q6.

True or False:True or False:

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

Page 13: 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.

A6.A6.

True True

Page 14: 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.

Q7.Q7.

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

Page 15: 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.

A7.A7.

slopeslope

y-intercepty-intercept

Page 16: 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.

Q8.Q8.

True or False:True or False:

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

Page 17: 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.

A8.A8.

True True

Page 18: 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.

Q9.Q9.

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

Page 19: 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.

A9.A9.

slopeslope

Page 20: 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.

Q10.Q10.

A function A function ff is _?_ on an is _?_ on an open interval if for any open interval if for any choice of choice of xx

11 and and xx

22 in the in the

interval, with interval, with xx11<<xx

22, we , we

have have f(xf(x11)) < < f(xf(x

22))..

Page 21: 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.

A10.A10.

increasingincreasing

Page 22: 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.

Q11.Q11.

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

Page 23: 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.

A11.A11.

eveneven

Page 24: 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.

Q12.Q12.

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

Page 25: 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.

A12.A12.

oddodd

Page 26: 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.

Q13.Q13.

True or False:True or False:

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

Page 27: 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.

A13.A13.

falsefalse

Page 28: 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.

Q14.Q14.

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

Page 29: 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.

A14.A14.

lessless

Page 30: 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.

Q15.Q15.

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

Page 31: 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.

A15.A15.

piecewisepiecewise

Page 32: 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.

Q16.Q16.

True or False:True or False:

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

Page 33: 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.

A16.A16.

truetrue

Page 34: 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.

Q17.Q17.

True or False:True or False:

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

Page 35: 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.

A17.A17.

falsefalse

Page 36: 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.

Q18.Q18.

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

Page 37: 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.

A18.A18.

horizontalhorizontal

rightright

Page 38: 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.

Q19.Q19.

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

Page 39: 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.

A19.A19.

yy

Page 40: 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.

Q20.Q20.

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

Page 41: 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.

A20.A20.

stretchstretch

33

Page 42: 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.

Q21.Q21.

True or False:True or False:

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

Page 43: 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.

A21.A21.

truetrue

Page 44: 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.

Q22.Q22.

True or False:True or False:

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

Page 45: 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.

A22.A22.

falsefalse

Page 46: 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.

Q23.Q23.

True or False:True or False:

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

Page 47: 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.

A23.A23.

truetrue

Page 48: 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.

Q24.Q24.

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

Page 49: 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.

A24.A24.

[0,5][0,5]

Page 50: 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.

Q25.Q25.

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

Page 51: 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.

A25.A25.

≠≠

ff

gg

Page 52: 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.

Q26.Q26.

If If f(x) = x + 1f(x) = x + 1 and and g(x) = x³g(x) = x³, then , then _?_ _?_ = (x + 1)³ .= (x + 1)³ .

Page 53: 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.

A26.A26.

g(f(x))g(f(x))

Page 54: 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.

Q27.Q27.

True or False:True or False:

f(g(x)) = f(x)· g(x)f(g(x)) = f(x)· g(x)

Page 55: 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.

A27.A27.

falsefalse

Page 56: 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.

Q28.Q28.

True or False:True or False:

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

Page 57: 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.

A28.A28.

truetrue

Page 58: 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.

Q29.Q29.

True or False:True or False:

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

Page 59: 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.

A29.A29.

falsefalse

Page 60: 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.

Q30.Q30.

What is the best What is the best way to study way to study

for a Math test?for a Math test?

Page 61: 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.

A30.A30.

Work problems!Work problems!


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