Chapter 2 ReviewChapter 2 Review

Concepts and VocabularyConcepts and Vocabulary

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.

A1.A1.

independentindependent

dependentdependent

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.

A2.A2.

verticalvertical

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 _?_.

A3.A3.

rangerange

Q4.Q4.

True or False:True or False:

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

A4.A4.

FalseFalse

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)..

A5.A5.

True True

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.

A6.A6.

True True

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 _?_.

A7.A7.

slopeslope

y-intercepty-intercept

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.

A8.A8.

True True

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.

A9.A9.

slopeslope

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))..

A10.A10.

increasingincreasing

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..

A11.A11.

eveneven

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..

A12.A12.

oddodd

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.

A13.A13.

falsefalse

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.

A14.A14.

lessless

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.

A15.A15.

piecewisepiecewise

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 (- ∞, ∞).

A16.A16.

truetrue

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.

A17.A17.

falsefalse

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 _?_._?_.

A18.A18.

horizontalhorizontal

rightright

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)..

A19.A19.

yy

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 _?_.

A20.A20.

stretchstretch

33

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)..

A21.A21.

truetrue

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.

A22.A22.

falsefalse

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.

A23.A23.

truetrue

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 _?_._.

A24.A24.

[0,5][0,5]

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 _?_.

A25.A25.

≠≠

ff

gg

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 .

A26.A26.

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

Q27.Q27.

True or False:True or False:

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

A27.A27.

falsefalse

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..

A28.A28.

truetrue

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)..

A29.A29.

falsefalse

Q30.Q30.

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

for a Math test?for a Math test?

A30.A30.

Work problems!Work problems!