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MTH107Exam5Reviewsp20.pdf
MTH107 EXAM 5 REVIEW - SPRING 2020
This is a collection of questions to use as a review for the MTH107 Cumulative Exam 5. This exam will be composed of 10 multiple choice questions and 5 open-ended questions. You must show supporting work for the open-ended questions. In addition to the questions given here, the tests given throughout the semester should also be used in reviewing for the final exam.
Solve the system of equations by using substitution. Graph the equation and label the points of intersection.
1) 5x - 2y = -1 x + 4y = 35
Solve the system of equations by using substitution. Graph the equation and label the points of intersection. 2)
y = x2 - 3 x2 + y2 = 5
3) y = x2 - 12x + 36 x + y = 8
Find the domain of the function.
4) h(x) = x - 3
x3 - 81x
Find the domain of the rational function.
5) f(x) = x(x - 1)
25x2 + 30x + 8
Solve the problem.
6) What is the domain of the function f(x) = x - 9 x + 4
?
Solve the equation. 7) x + 7 - 2 = 13
Solve the inequality. Express your answer using interval notation. Graph the solution set. 8) |7k + 2| - 3 > 4
1
9) |7k + 7| + 8 < 16
Find the linear factorization of the polynomial and find all roots of the polynomial. Show all work including division. 10) f(x) = x4 - 9x3 + 24x2 - 36x + 80
11) f(x) = x3 + 6x2 + 7x + 42
12) f(x) = x3 + 8x2 + 25x + 200
Find and simplify the difference quotient of f, f(x + h) - f(x)
h , h 0, for the function.
13) f(x) = 4x2 + 9x - 1
Find and simplify the difference quotient of f, f(x + h) - f(x)
h , h 0, for the function.
14) f(x) = x2 + 5x + 8
Find and simplify the difference quotient of f, f(x + h) - f(x)
h , h 0, for the function.
15) f(x) = 1 3x
Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
16) f(x) = -3(x + 1)2 + 3
17) f(x) = 1
x + 2
18) f(x) = x + 3 - 7
19) f(x) = |x + 3| + 6
Solve the problem. 20) Sue wants to put a rectangular garden on her property using 74 meters of fencing. There is a river that runs
through her property so she decides to increase the size of the garden by using the river as one side of the rectangle. (Fencing is then needed only on the other three sides.) Let x represent the length of the side of the rectangle along the river. Express the garden's area as a function of x.
2
21) A wire of length 7x is bent into the shape of a square. Express the area A of the square as a function of x.
22) A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 14 inches by 28 inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x.
28
14
Graph the function. Label its vertex, axis of symmetry, and intercepts. State the minimum or maximum value of the function. Find the intervals of increase and decrease.
23) f(x) = -x2 + 6x - 8
Graph the function. Label its vertex, axis of symmetry, and intercepts. State the minimum or maximum value of the function. Find the intervals of increase and decrease.
24) f(x) = -2x2 - 8x - 12
3
Graph the function. Label its vertex, axis of symmetry, and intercepts. State the minimum or maximum value of the function. Find the intervals of increase and decrease.
25) f(x) = 4x2 + 16x + 19
Graph the function. Label all asymptotes and intercepts. Show all work.
26) f(x) = x2 + x - 56 x2 - x - 42
27) f(x) = x
x2 - 64
4
28) f(x) = 2x
(x + 3)(x + 5)
Find the real zeros, if any, of each quadratic function using the quadratic formula. List the x-intercepts, if any, of the graph of the function.
29) g(x) = x2 - 12 - 5x
30) F(x) = 3x2 - 7x - 1
31) F(x) = 5x2 - 7x - 1
Solve the inequality. Express the solution using interval notation. Show all work including number line tests. 32) x3 + 2x2 - 8x > 0
33) 12
x - 5 >
10 x - 1
Solve the inequality. Express the solution using interval notation. Show all work including number line tests.
34) x + 28 x + 2
< 6
Find the inverse function of f. State the domain and range of f and f-1.
35) f(x) = 3x - 2 x + 5
The function f is one-to-one. Find its inverse.
36) f(x) = -5x - 7 7x - 2
5
37) f(x) = 2
x - 3
Graph the function.
38) f(x) = 4(x - 3) + 1
39) f(x) = 3 - e-x
Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. 40) f(x) = -2x+3 + 4
Solve the equation.
41) 2x2 - 3= 64
42) e x + 3
= 5
Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places.
43) 5 4
x = 31 - x
Solve the equation. 44) log20 (x2 - x) = 1
45) log 2 (x + 3) = 2 + log 2 (x - 3)
46) log 2 (x - 5) + log 2 (x - 11) = 4
6
Answer Key Testname: MTH107 EXAM 5 REVIEW SP20
1) x = 3, y = 8 2) x = -2, y = 1; x = -1, y = -2; x = 1, y = -2; x = 2, y = 1 3) x = 7, y = 1; x = 4, y = 4 4) {x|x -9, 0, 9}
5) x x - 2 5
, - 4 5
6) ( , -4) or [9, ) 7) {-22, 8}
8) (- , - 9 7
) ( 5 7
, )
9) (- 15 7
, 1 7
)
10) f(x) = (x - 5)(x - 4)(x + 2i)(x - 2i), roots: 5, 4, ± 2i 11) f(x) = (x + 6)(x + i 7)(x - i 7), roots: -6, ± i 7 12) f(x) = (x + 8)(x + 5i)(x - 5i), roots: -8, ± 5i 13) 8x + 4h + 9 14) 2x+ h + 5
15) -1
3x (x + h) 16)
7
Answer Key Testname: MTH107 EXAM 5 REVIEW SP20
17)
18)
19)
20) A(x) = 37x - 1 2
x2
21) A(x) = 49 16
x2
22) V(x) = x(14 - 2x)(28 - 2x)
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Answer Key Testname: MTH107 EXAM 5 REVIEW SP20
23) vertex (3, 1) intercepts (4, 0), (2, 0), (0, -8)
24) vertex (-2, -4) intercept (0, -12)
25) vertex (-2, 3) intercept (0, 19)
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Answer Key Testname: MTH107 EXAM 5 REVIEW SP20
26)
27)
28)
29) x = 5 ± 73
2
30) x = 7 ± 61
6
31) x = 7 ± 69
10 32) (-4, 0) or (2, )
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Answer Key Testname: MTH107 EXAM 5 REVIEW SP20
33) (-19, 1) or (5, )
34) - , -2 or 16 5
,
35) f-1(x) = 5x + 2 3 - x
; domain of f: {x x -5}; range of f: {y y 3}
36) f-1(x) = 2x - 7 7x + 5
37) f-1(x) = 3x + 2
x 38)
39)
40) domain of f: (- , ); range of f: (- , 4); horizontal asymptote: y = 4
11
Answer Key Testname: MTH107 EXAM 5 REVIEW SP20
41) {3, -3} 42) {ln 5 - 3}
43) ln 3
ln 5 4
+ ln 3 0.831
44) {-4, 5} 45) 5 46) {13}
12
