Review for Exam 2 (2.4-2.8, 3.1-3.6)
Name___________________________________
Write the equation in slope-intercept form and determine the slope and y-intercept.
1) -2x = -3y - 6
1)
Use the slope-intercept form to write an equation of the line that passes through the given point and has
the given slope. Use function notation where y = f(x).
2) (9, -3); m = 0
2)
Determine the average rate of change of the function on the given interval.
3) f (x) = x3 + 3 on [2, 3]
3)
Use the point-slope formula to write an equation of the line that passes through the given points. Write
the answer in slope-intercept form (if possible).
4) (3, -3) and (-4, -5)
4)
Write an equation of the line satisfying the given conditions. Write the answer in standard form with no
fractional coefficients.
5) Passes through (-1, -4) and is parallel to the line defined by 5x + 3y = -8
5)
Find the slope of the secant line indicated with a dashed line.
6)
6)
Write an equation of the line satisfying the given conditions. Write the answer in standard form with no
fractional coefficients.
7) Passes through (4, 4) and is perpendicular to the line defined by -5x + 4y = -6
7)
1
Use transformations to graph the given function.
8) f(x) = -(x + 3)2 + 2
8)
A function g is given. Identify the parent function. Then use the steps for graphing multiple
transformations of functions to list, in order, the transformations applied to the parent function to obtain
the graph of g.
9) g(x) =
1
(x + 1.3)2 - 2.5
5
9)
Find f(-x) and determine whether f is odd, even, or neither.
10) f (x) = 4x5 - 5x4
10)
Determine if the function is odd, even, or neither.
3
- x
11) f (x) =
8x 2
Solve the problem.
12) Use interval notation to write the intervals over which f is constant
2
12)
Identify the location and value of any relative maxima or minima of the function.
13)
13)
Evaluate the function for the given value of x.
14) f (x) = x2 + 3x, g(x) = 5x + 2, (f g)(3) = ?
14)
Find the indicated function and write its domain in interval notation.
1
, (q n)(x) = ?
15) n(x) = x + 3, q(x) =
x+6
15)
Find the vertex of the parabola.
16) f (x) = x2 + 16x - 8
16)
Determine the x- and y-intercepts for the given function.
17) f (x) = 2x2 + 8x - 10
17)
Identify the vertex, axis of symmetry, and intercepts for the graph of the function.
18) y = x2 + 8x + 14
18)
Find the vertex of the parabola by applying the vertex formula.
1
19) f (x) = - x2 - 6x - 7
5
Use long division to divide.
64x3 + 1
20)
4x + 1
19)
20)
Use synthetic division to divide the polynomials.
21) (7w 3 + 2w 2 - 3w - 14) ÷ (w - 1)
21)
3
Use the remainder theorem to evaluate the polynomial for the given value of x.
22) f (x) = 3x4 - 7x3 - 7x2 + 42x - 19; f (3)
22)
Use the remainder theorem to determine if the given number c is a zero of the polynomial.
23) x4 + 9x3 + 22x2 + 19x + 45; c = -3
23)
Write a polynomial f (x) that meets the given conditions. Answers may vary.
24) Degree 3 polynomial with zeros 4, 5i, and -5i
24)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
List the possible rational zeros.
25) f (x) = 25x4 - 7x3 + 2x + 10
5
25
1
1
, ±5, ± , ±25, ±
A) ±1, ± , ±
5 25
2
2
1
5
C) ±1, ± , ±
25)
2
2
1
1
, -5, -2, - , B) -1, - , 5 25
5 25
2
2
1
, ±5, ±2, ±10, ± , ±
25
5 25
D) 1,
2 2
1 1
,
, 5, 2, ,
5 25
5 25
Write a polynomial f (x) that meets the given conditions. Answers may vary.
26) Degree 2 polynomial with zeros 3 5 and -3 5
26)
Solve the inequality. Write the solution set in interval notation.
27) (7x - 9)(5x - 9) < 0
27)
28) 7y2 + 5y
29) (x
28)
-9(7y + 5)
+ 7)(x + 11)
29)
-4
A polynomial f (x) and one of its zeros are given. Factor f (x) as a product of linear factors.
3 + 2i is a zero
30) f (x) = 4x3 - 23x2 + 46x + 13;
30)
Solve the problem.
31) Determine if the lower bound theorem identifies -4 as a lower bound for the real
zeros of f (x).
31)
f (x) = 3x3 + 2x2 - 9x + 4
Determine the number of possible positive and negative real zeros for the given function.
32) f (x) = -8x7 - 7x4 - 6x3 + 4x2 + 6x + 5
32)
4
Solve the inequality. Write the solution set in interval notation.
7x
7
33)
x+2
Identify the asymptotes.
4x + 5
34) r(x) =
3
x - 5x2 - 9x + 45
35) f (x) =
33)
34)
x3 - 4x2 - 9x + 8
35)
x2 - 6
Find the center and radius of the circle.
36) 4x2 + 4y2 + 8x + 32y + 4 = 0
36)
Use the given information about a circle to write an equation of the circle in standard form.
37) The center is (-5, -4) and another point on the circle is (1, 4)
37)
Determine the intervals on which the function is increasing, decreasing, and constant.
38)
5
38)
Graph the function.
x2 - 4
39) f(x) = 0
x2 + 4
for x < -1
for -1 x 1
for x > 1
Solve the problem.
40) A deep sea diving bell is being lowered at a constant rate. After 9 minutes, the bell is at a
depth of 500 feet. After 50 minutes the bell is at a depth of 1500 feet. What is the average
rate of lowering per minute?
Write the equation of the graph after the indicated transformation(s).
41) The graph of y = x2 is translated 6 units to the left and 4 units downward.
42) The graph of y =
x is shifted 10 units to the left. Then the graph is shifted 4 units upward.
40)
41)
42)
Find the center-radius form of the circle described or graphed.
43) a circle having a diameter with endpoints (-6, -6) and (1, -1)
43)
Find the function value.
44)
44)
f
f(-6) for the function f
Find the requested composition of functions.
7
4
and g(x) =
, find (f g)(x).
45) Given f(x) =
x-4
7x
45)
6
Give the domain and range of the relation.
46)
46)
Find the domain and range.
x+1
47) f(x) =
x+1
47)
Write an equation for the line described. Write the equation in the form specified.
48) parallel to y + 2x = 4, through (5, 3); slope-intercept form
49) perpendicular to -3x + y = 2, through (2, 3); slope-intercept form
48)
49)
Determine whether the equation defines y as a function of x.
50) x = 5y
50)
List the symmetries of the given function, if there are any. Otherwise, state "No symmetry".
51) f(x) = 5x + 3
51)
Evaluate.
52) Given f(x) = 3x - 2 and g(x) = -9x + 10, find (f - g)(x).
52)
53) Find (f/g)(-3) given f(x) = 4x - 3 and g(x) = 3x2 + 14x + 4.
53)
54) Find f(k - 1) when f(x) = 5x2 - 3x + 5.
54)
7
Use the graph of y = f(x) to find the function value.
55) f(-2)
55)
Write an equation of the line. Write the equation in the form x = a, y = b, or y = mx + b.
56) Through (-2, 12); perpendicular to 5x + 9y = 58
56)
Determine whether the function is even, odd, or neither.
57) f(x) = x2 + x
57)
Find an equation of the line passing through the two points. Write the equation in standard form.
58) (8, -6) and (-1, 5)
58)
Write an equation for the line described. Give your answer in slope-intercept form.
8
59) m = - , through (2, -9)
9
Find functions f and g so that F(x) = (f g) (x).
7
60) F(x) =
7x + 10
59)
60)
Solve the inequality.
x + 17
<2
61)
x+8
61)
8
Answer Key
Testname: REVIEW FOR EXAM 2 FALL 2017
1) y =
2
2
x - 2; slope: ; y-intercept: (0, -2)
3
3
2)
f(x) = -3
3) 19
2
27
4) y = x 7
7
5)
5x + 3y = -17
9
6) m =
4
7)
4x + 5y = 36
8)
9) Parent function: f (x) = x2 ; Shift the graph of f to the left 1.3 units, shrink the graph vertically by a factor
of
1
, and shift the graph downward by 2.5 units.
5
10) f (-x) = -4x5 - 5x4 ; f is neither odd nor even.
11) Odd
12) (-1,
2)
13) At x = -3, the function has a relative minimum of -5.
At x = 0, the function has a relative maximum of 0.
At x = 3, the function has a relative minimum of -5.
14) ( f g)(3) = 340
1
; domain: (- , -9) (-9, )
15) (q n)(x) =
x+9
16) (-8,
-72)
17) x-intercepts: (-5, 0) and (1, 0)
y-intercept: (0, -10)
18) Vertex at (-4, -2); axis: x = -4; x-intercepts: (-4 - 2, 0) and (-4 + 2, 0) ; y-intercept: (0, 14)
9
Answer Key
Testname: REVIEW FOR EXAM 2 FALL 2017
19) (-15, 38)
20) 16x2 - 4x + 1
21) 7w 2 + 9w + 6 -
8
w-1
22) 98
23) No
24) f (x) = x3 - 4x2 + 25x - 100
25) C
26) f (x) = x2 - 45
27)
9 9
,
7 5
28) -9, -
5
7
29) {-9}
30) (4x
+ 1)(x - (3 + 2i))(x - (3 - 2i))
31) Yes
32) Positive: 1; Negative: 4 or 2
33) (- , -2)
34) Vertical asymptotes: x = -3, x = 3, and x = 5; horizontal asymptote: y = 0
35) Vertical asymptotes: x = 6 and x = - 6
Slant asymptote: y = x - 4
36) center: (-1, -4), radius: 4
37) (x + 5)2 + (y + 4)2 = 100
38) Increasing on (-2, 0) and (3, 5); Decreasing on (1, 3); Constant on (-5, -2)
39)
40) 24.4 ft per minute
41) y = (x + 6)2 - 4
42) y =
x + 10 + 4
5 2
7 2 37
+ y+
=
43) x +
2
2
2
10
Answer Key
Testname: REVIEW FOR EXAM 2 FALL 2017
44) 15
49x
45)
4 - 28x
46) domain: [-3, 0]; range: [-3, 1]
47) D = (- , -1) (-1, ) , R = -1, 1
48) y = - 2x + 13
1
11
49) y = - x +
3
3
50) No
51) y-axis
52) 12x - 12
15
53)
11
54) 5k2 - 13k + 13
55) 1
78
9
56) y = x +
5
5
57) Neither
58) 11x + 9y = 34
8
65
59) y = - x 9
9
60) f(x) =
61) - , -8
7
, g(x) = 7x + 10
x
1,
11