Exam 2 Review
Determine whether the relation is a function and give the domain and range of the relation.
1) {(-7, -8), (-7, -5), (2, 2), (4, -8), (10, 6)}
Determine whether the relation is a function.
2) {(-6, 9), (-3, 6), (2, 2), (8, 4)}
3) {(1, 5), (2, 3), (5, -3), (7, -3), (11, 7)}
Determine whether the equation defines y as a function of x.
4) x2 + y = 16
5) x2 + y2 = 9
6) x + y3 = 27
Evaluate the function at the given value of the independent variable and simplify.
f(x - 4)
7) f(x) = x2 - 3;
8) f(x) = 3x 2 - 3x - 4;
9) f(x) =
x2 + 6
;
x3 - 5x
f(x - 1)
f(-4)
Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
10)
1
11)
12)
13)
2
14)
Use the graph to determine the function's domain and range.
15)
16)
3
17)
18)
18)
A) domain: (- , )
range: [0, 6]
B) domain: [0, 6]
range: (- , )
C) domain: (- , )
range: [3, 6]
Identify the intercepts.
19)
4
D) domain: [3, 6]
range: (- , )
20)
Identify the intervals where the function is changing as requested.
21) Constant
22) Decreasing
5
23) Constant
Use the graph of the given function to find any relative maxima and relative minima.
24) f(x) = x3 - 3x2 + 1
Determine whether the given function is even, odd, or neither.
25) f(x) = 2x 2 + x4
26) f(x) = x3 + x2 + 3
6
Use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a function
that is neither even nor odd.
27)
28)
29)
Evaluate the piecewise function at the given value of the independent variable.
30) f(x) = 3x - 2 if x < 1 ; f(1)
2x + 3 if x 1
if x > -3 ; f(-5)
31) f(x) = x - 1
1)
if
x -3
-(x -
7
Graph the function.
32) f(x) = -x + 3
2x - 3
if x < 2
if x 2
Find and simplify the difference quotient
f(x + h) - f(x)
,h
h
0 for the given function.
33) f(x) = 3x 2
34) f(x) = x2 + 8x - 9
Use the given conditions to write an equation for the line in point-slope form.
35) Slope = 3, passing through (-7, 8)
36) Passing through (1, -5) with x-intercept = -1
Use the given conditions to write an equation for the line in slope-intercept form.
37) Slope = 2, passing through (-6, 3)
38) Passing through (-8, -3) and (-4, -8)
Use the given conditions to write an equation for the line in the indicated form.
39) Passing through (3, 2) and parallel to the line whose equation is y = 2x - 6;
point-slope form
40) Passing through (4, 5) and perpendicular to the line whose equation is y = 4x + 7;
point-slope form
Find the average rate of change of the function from x 1 to x 2 .
41) f(x) = -3x2 - x from x1 = 5 to x2 = 6
42) f(x) = 5x + 7 from x 1 = -1 to x2 = 0
8
Begin by graphing the standard quadratic function f(x) = x 2 . Then use transformations of this graph to graph the given
function.
43) h(x) = (x - 3)2 + 4
44) g(x) = -
1
(x - 5)2 + 3
3
Begin by graphing the standard absolute value function f(x) = x . Then use transformations of this graph to graph the
given function.
1
45) g(x) = x - 2 + 5
3
9
Use the graph of the function f, plotted with a solid line, to sketch the graph of the given function g.
46) g(x) = f(x + 1) + 1
y = f(x)
Given functions f and g, perform the indicated operations.
47) f(x) = 9x 2 - 5x, g(x) = x2 - 3x - 10
Find
f
.
g
48) f(x) = 5x - 2,
Find fg.
g(x) = 6x + 3
Find the domain of the indicated combined function.
f
(x) when f(x) = 7x2 - 9x and g(x) = x2 - 4x - 7.
49) Find the domain of
g
For the given functions f and g , find the indicated composition.
g(x) = 7x - 8
50) f(x) = 14x2 - 10x,
(f g)(9)
51) f(x) = -4x + 2,
(g f)(x)
g(x) = 5x + 8
52) f(x) = 4x2 + 2x + 8,
(g f)(x)
g(x) = 2x - 4
Find functions f and g so that h(x) = (f
53) h(x) = |6x + 8|
54) h(x) =
g)(x).
10
7x + 6
Find the inverse of the one-to-one function.
8x + 5
55) f(x) =
3
10
56) f(x) =
57) f(x) =
7
3x - 1
3
x-3
Does the graph represent a function that has an inverse function?
58)
Use the graph of f to draw the graph of its inverse function.
59)
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval
notation.
60) x2 - 8x + 12 > 0
61) (x + 5)(x + 2)(x - 4) > 0
62) x3 + 3x2 - x - 3 > 0
11
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval
notation.
-x + 4
0
63)
x-2
64)
x+7
<3
x+8
65)
5x
<x
x+7
12
Answer Key
Testname: CAE2 HCC REVIEW
1)
2)
3)
4)
5)
6)
Not a function; Domain = {-8, -5, 2, 6}; Range = {-7, 2, 4, 10}.
Function
Function
y is a function of x
y is not a function of x
y is a function of x
7) x2 - 8x + 13
8) 3x2 - 9x + 2
9) 10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
1
2
not a function
function
function
not a function
not a function
domain: (- , )
range: [-2, )
domain: (- , )
range: (- , 3]
domain: [0, )
range: [2, )
A
(3, 0), (0, 6)
(6, 0), (-6, 0), (0, 4), (0, -4)
(- , -1) or (3, )
(- , 3)
(-1, 1)
maximum: (0, 1); minimum: (2, -3)
Even
Neither
Even
Neither
Odd
5
6
33) 3(2x+h)
13
Answer Key
Testname: CAE2 HCC REVIEW
34) 2x + h + 8
35) y - 8 = 3(x + 7)
5
5
36) y + 5 = - (x - 1) or y = - (x + 1)
2
2
37) y = 2x + 15
5
38) y = - x - 13
4
39) y - 2 = 2(x - 3)
1
40) y - 5 = - (x - 4)
4
41) -34
42) 5
43)
44)
45)
14
Answer Key
Testname: CAE2 HCC REVIEW
46)
47)
9x2 - 5x
2
x - 3x - 10
30x 2 + 3x - 6
Domain: - , 2 - 11
241,800
-20x + 18
52) 8x2 + 4x + 12
53) f(x) = |x|, g(x) = 6x + 8
54) f(x) = 10/ x, g(x) = 7x + 6
3x - 5
55) f-1 (x) =
8
48)
49)
50)
51)
11, 2 +
11
2+
11,
7
1
+
56) f-1 (x) =
3x 3
57) f-1 (x) = x3 + 3
58) No
59)
60) (- , 2) (6, )
61) (-5, -2) (4, )
15
Answer Key
Testname: CAE2 HCC REVIEW
62) (- 3, -1)
(1, )
63) (2, 4]
64) (- , -8) or (-
65) (-7, -2)
17
, )
2
(0, )
16