Lesson
Functions and Their Graphs
Determine whether the relation represents a function. If it is a function, state the domain and range.
1) {(29, -2), (4, -1), (4, 0), (5, 1), (13, 3)}
Determine whether the following equations define y as a function of x:
2) y = |x|
3)
x = y2
Find the value for the functions:
x2 - 8
4) Find f(2) when f(x) =
.
x+3
Find the value for the function.
5) Find f(-9) when f(x) = |x|- 6.
6)
Find f(x - 1) when f(x) = 5x2 - 5x - 4.
Solve the problems:
7) If f(x) = 5x3 + 2x2 - x + C and f(-3) = 1, what is the value of C?
x - 3A
and f(-3) = 9, what is the value of A?
-3x + 5
8)
If f(x) =
9)
9
The function F described by F(C) = C + 32 gives the Fahrenheit temperature corresponding to the
5
Celsius temperature C. Find the Fahrenheit temperature equivalent to 10°C.
Find the domain of the functions:
x
10) f(x)
=
11) g(x)
=
12) f(x)
= 10 - x
College Algebra
x2 + 12
3x
x2 - 64
Find the domain of the function.
13) f(x) = 23 - x
Find the domain of the functions:
x
14)
x-2
Find and simplify the difference quotient of f,
15) f(x)
= 9x + 9
16) f(x)
=
f(x + h) - f(x)
, h≠ 0, for the functions:
h
1
4x
Solve the problem.
function f(t) = -0.13t2 + 0.53t + 30.1 models the U.S. population in millions, ages 65 and older,
where t represents years after 1990. The function g(t) = 0.51t2 + 12.36t + 105.2 models the total
17) The
yearly cost of Medicare in billions of dollars, where t represents years after 1990. What does the
g
g
function represent? Find (5).
f
f
Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the
intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.
18)
5
y
5 x
-5
-5
Answer the question about the given functions:
19) Given the function f(x) = 2x2 - 4x - 2, is the point (1, -4) on the graph of f?
20) Given
College Algebra
the function f(x) = x2 + 4x - 32, list the x-intercepts, if any, of the graph of f.
21) Given
College Algebra
the function f(x) =
x2 - 4
, is the point (2, - 8) on the graph of f?
x-3
Answer Key
Testname: 7_FUNCTIONS_AND_GRAPHS
1) not a function
2) function
3) not a function
4
4) - 5
5) 3
6) 5x2 - 15x + 6
7) C = 115
8) A = -43
9) 50°F
10) all real numbers
11) {x|x ≠ -8, 8}
12) {x|x ≤ 10}
13) {x|x ≤ 23}
14) {x|x > 2}
15) 9
-1
16) 4x (x + h)
17) Cost per person in thousands of dollars. $6.09
thousand
18) function
domain: {x|x ≥ -2}
range: {y|y ≤ 0}
intercepts: (-2, 0), (0, -2), (2, 0)
symmetry: none
19) Yes
20) (-8, 0), (4, 0)
21) No
College Algebra