CHAPTER 1: SECTION CONCEPT CHECK
TABLE OF CONTENTS
End of Section Exercise Solutions.............................................................................................................. 1
END OF SECTION EXERCISE SOLUTIONS
1.CV.1
(a) A function f is a rule that assigns to each element x in a set D (the domain) exactly one element,
called f ( x ), in a set E. The set of inputs for the function, D, is the domain. The range of f is the set of
all possible values of f ( x ) as x varies throughout the domain.
(b) To obtain the graph of the function f, plot the ordered pairs of points,
( x, f ( x) ).
(c) A curve is the graph of a function if it passes the Vertical Line Test – that is, if no vertical line
intersects the curve more than once.
1.CV.2
There are four ways to represent a function:
• Verbally: C ( w) is the cost of mailing a large envelope of weight w.
• Numerically (with a table of values):
1|Page
, • Visually (with a graph):
• Algebraically: y = f ( x) = x + 1
2
1.CV.3
(a) f is an even function if for every x in its domain, f (− x) = f ( x). The graph of an even function is
symmetric with respect to the y-axis. Examples of even functions include y = x , y = − x , and
2 2
y = cos x.
(b) f is an odd function if for every x in its domain, f (− x) = − f ( x). The graph of an even function is
symmetric about the origin. Examples of even functions include y = x , y = x + x, and y = sin x.
3 5
1.CV.4
A function f is increasing on an interval I if f ( x1 ) f ( x2 ) whenever x1 x2 in I.
1.CV.5
A mathematical model is a mathematical description of a real-world phenomenon. The purpose of the
model is to understand the phenomenon and perhaps to make predictions about future behavior.
1.CV.6
(a) y = 2 x + 5 is a linear function.
(b) y = x is a power function.
7
(c) y = e is an exponential function.
x
(d) y = x − 3x + 13 is a quadratic function.
2
(e) y = x − 3x + 7 x − 12 is a polynomial of degree 5.
5 4
x−3
(f) y = is a rational function.
x+7
2|Page
,1.CV.7
1.CV.8
(a) y = sin x (b) y = tan x
(c) y = e (d) y = ln x
x
(e) y = 1/ x (f) y = x
3|Page
, −1
(g) y = x (h) y = tan x
1.CV.9
(a) The domain of f + g is A B.
(b) The domain of fg is A B.
(c) The domain of f / g is {x | x A B and g ( x) 0}.
1.CV.10
The composite of f and g is ( f g )( x) = f ( g ( x)) and its domain is the set of all x in the domain of g
such that g ( x ) is in the domain of f.
1.CV.11
(a) If the graph of f is shifted 2 units upward, its equation becomes y = f ( x ) + 2 .
(b) If the graph of f is shifted 2 units downward, its equation becomes y = f ( x ) − 2 .
(c) If the graph of f is shifted 2 units to the right, its equation becomes y = f ( x − 2) .
(d) If the graph of f is shifted 2 units to the left, its equation becomes y = f ( x + 2 ) .
4|Page
TABLE OF CONTENTS
End of Section Exercise Solutions.............................................................................................................. 1
END OF SECTION EXERCISE SOLUTIONS
1.CV.1
(a) A function f is a rule that assigns to each element x in a set D (the domain) exactly one element,
called f ( x ), in a set E. The set of inputs for the function, D, is the domain. The range of f is the set of
all possible values of f ( x ) as x varies throughout the domain.
(b) To obtain the graph of the function f, plot the ordered pairs of points,
( x, f ( x) ).
(c) A curve is the graph of a function if it passes the Vertical Line Test – that is, if no vertical line
intersects the curve more than once.
1.CV.2
There are four ways to represent a function:
• Verbally: C ( w) is the cost of mailing a large envelope of weight w.
• Numerically (with a table of values):
1|Page
, • Visually (with a graph):
• Algebraically: y = f ( x) = x + 1
2
1.CV.3
(a) f is an even function if for every x in its domain, f (− x) = f ( x). The graph of an even function is
symmetric with respect to the y-axis. Examples of even functions include y = x , y = − x , and
2 2
y = cos x.
(b) f is an odd function if for every x in its domain, f (− x) = − f ( x). The graph of an even function is
symmetric about the origin. Examples of even functions include y = x , y = x + x, and y = sin x.
3 5
1.CV.4
A function f is increasing on an interval I if f ( x1 ) f ( x2 ) whenever x1 x2 in I.
1.CV.5
A mathematical model is a mathematical description of a real-world phenomenon. The purpose of the
model is to understand the phenomenon and perhaps to make predictions about future behavior.
1.CV.6
(a) y = 2 x + 5 is a linear function.
(b) y = x is a power function.
7
(c) y = e is an exponential function.
x
(d) y = x − 3x + 13 is a quadratic function.
2
(e) y = x − 3x + 7 x − 12 is a polynomial of degree 5.
5 4
x−3
(f) y = is a rational function.
x+7
2|Page
,1.CV.7
1.CV.8
(a) y = sin x (b) y = tan x
(c) y = e (d) y = ln x
x
(e) y = 1/ x (f) y = x
3|Page
, −1
(g) y = x (h) y = tan x
1.CV.9
(a) The domain of f + g is A B.
(b) The domain of fg is A B.
(c) The domain of f / g is {x | x A B and g ( x) 0}.
1.CV.10
The composite of f and g is ( f g )( x) = f ( g ( x)) and its domain is the set of all x in the domain of g
such that g ( x ) is in the domain of f.
1.CV.11
(a) If the graph of f is shifted 2 units upward, its equation becomes y = f ( x ) + 2 .
(b) If the graph of f is shifted 2 units downward, its equation becomes y = f ( x ) − 2 .
(c) If the graph of f is shifted 2 units to the right, its equation becomes y = f ( x − 2) .
(d) If the graph of f is shifted 2 units to the left, its equation becomes y = f ( x + 2 ) .
4|Page
