Math 1314 Test 1 REVIEW
Sections 1.7, 2.3 thru 2.8
Student Name: ____________________________
Solve the inequality. Write the solution set in interval notation.
1) -2(7y - 7) + y > 2y - (-5 + y)
Solve the absolute value inequality. Write the solution in interval notation.
2) 3|x - 9| + 9 < 15
3)
3|x + 10| - 12 < -9
4)
3|x - 5| + 12
15
5)
3|x - 4| - 12
-9
Determine whether the relation defines a function, then give its domain and range.
6)
Function? YES or NO
Domain: ________________
Range: __________________
1
7)
Function? YES or NO
Domain: ________________
Range: __________________
Write the domain in interval notation. Show algebraic work.
8)
a(x) = 8 - x
9) y (t ) =
19 - x
10) f(x) =
x+7
x+3
11) f(x) =
x+5
x-7
Evaluate the function for the indicated value, then simplify.
12) f (x) = 2x2 - 4x; find f (8)
13)
f (x) = 2x2 + 2x; find f (-3)
2
Use the graph of y = f (x) to answer the questions.
a. Determine f (-1)
b. Determine f (-2)
14)
c. Find all x for which f (x) = -4
Find the x- and y-intercepts.
15) -5x - 2y = 10
16) -3x
17) 2x
- 5y = 15
+ 5y = 10
Determine the slope of the line passing through the given points.
18) (8, -1) and (10, -7)
19) (-2,
-2) and (-2, 3)
Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept.
20) 3x = 3 - y
3
21) 4x + 5y = 20
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).
22) (4, 5); m = -3
23) (1,
-5); m = 2
Determine if the lines defined by the given equations are parallel, perpendicular, or neither.
24) -4y = 2x + 5
-4x = 8y + 3
25) -4y = -3x - 3
-12x = 9y + 8
Write an equation of the line satisfying the given conditions.
26) The line passes through (25, 24) and is perpendicular to y = 6.
27) Passes
through (4, 4) and is perpendicular to the line defined by -5x + 4y = -6
28) Passes
through (2, 4) and is perpendicular to the line defined by -3x + 2y = -4
Write a function based on the given parent function and the transformations in the given order.
29) Parent function: y = x3
1. Shift 6.8 units to the right.
2. Reflect across the y-axis.
3. Shift downward 5.2 units.
4
30) Parent function: y = x3
1. Shift 4.5 units to the left.
2. Reflect across the y-axis.
3. Shift downward 1.6 units.
31) Parent function: y =
1. Shift 5 units to the left.
2. Reflect across the y-axis.
3. Shift 7 units upward.
Provide the missing information.
32) The graph of y = f (3x) is the graph of y = f (x) with a ____________________
vertical stretch
vertical shrink
horizontal stretch
horizontal shrink
33) The graph of y = 3f (x) is the graph of y = f (x) with a ____________________
vertical stretch
vertical shrink
horizontal stretch
Find f(-x) and determine whether f is odd, even, or neither.
34) f (x) = 2x4 + 3x2
35) f (x) = 4x5 - 5x4
36) f (x) = 2x4 - 3x2
37) f (x) = 3x4 + 2x3
Evaluate the function for the given values of x.
38)
-5x + 4, for x < -1
f(x) = x2 + 3,
1,
(a) f(-1); (b) f(3)
for -1 x < 2
for x 2
39) Evaluate f (-1) ; f (7)
f (x) =
9
x+1
-5
x -1
-1 < x 5
x>5
5
horizontal shrink
40)
f (x) =
7
x+1
-5
x -1
-1 < x 5
x>5
Evaluate f (0); f (3)
Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant.
41)
Evaluate the function for the given value of x.
42) r (x) = 3x, p (x) = x 2 + 6x, (p - r)(x)
43) f (x) = x2 and g(x) = 1; (f + g) (x).
44) p(x) = x2
+ 7x, q(x) = x + 3, (p q)(x) = ?
45) r (x) = -7x + 1, p (x) = x 2 + 3x, (p - r)(x)
46) g(x) =
3x, h(x) = x3 + 5x, (g h)(2) = ?
47) g(x) = 4x - 3, h(x) = 3 x - 7, (h
g)(1) = ?
48) n(x) = x + 3, q(x) =
1
, (q n)(x) = ?
x+6
49) n(x) = x + 1, q(x) =
1
, (q n)(x) = ? Evaluate and write domain in interval notation.
x+9
50) n(x) = x - 1, q(x) =
1
, (q n)(x) = ? Evaluate and write domain in interval notation.
x + 10
Evaluate and write domain in interval notation.
6
Answer Key
Testname: TEST 1 REVIEW PRINT
1)
,
9
14
2)
(7, 11)
3) (-11, -9)
4) (- , 4] [6, )
5) (- , 3] [5, )
6) Domain: (- , ); Range (- , 1]
7) Domain: (- , ); Range: [2, )
8) (- , 8]
9) (- , 19]
10) (- , -3) (-3, )
11) (- , 7) (7, )
12) 96
13) 24
14) f (-1) = 1; f (x) = -4 for all x on the interval (-1, 2)
15) x-intercept: (-2, 0);
y-intercept: (0, -5)
7
Answer Key
Testname: TEST 1 REVIEW PRINT
16) x-intercept: (-5, 0);
y-intercept: (0, -3)
17) x-intercept: (5, 0);
y-intercept: (0, 2)
18) m
= -3
19) Undefined
20) y = -3x + 3
8
Answer Key
Testname: TEST 1 REVIEW PRINT
21) y = -
4
x+4
5
22)
f(x) = -3x + 17
23) f(x) = 2x - 7
24) parallel
25) perpendicular
26) x = 25
27) 4x + 5y = 36
28) 2x + 3y = 16
29)
y = (-x - 6.8)3 - 5.2
30)
y = (-x + 4.5)3 - 1.6
31)
32) horizontal
shrink
stretch
34) f (-x) = 2x4 + 3x2 ; f is even.
35) f (-x) = -4x5 - 5x4 ; f is neither odd nor even.
33) vertical
36) f (-x) = 2x4 - 3x2 ; f is even.
37) f (-x) = 3x4 - 2x3 ; f is neither odd nor even.
38) (a)
4; (b) 1
39) 9
40) 7
41) a. (- , -2)
(2, )
b. never decreasing
c. (-2, 2)
42) (p - r)(x) = x 2 + 3x
43)
44) (p q)(x) = (x2 + 7x) x +
45) (p - r)(x) = x 2 + 10x - 1
3
9
Answer Key
Testname: TEST 1 REVIEW PRINT
46) 3 6
47) Undefined
48) (q
n)(x) =
1
; domain: (- , -9) (-9, )
x+9
49) (q
n)(x) =
1
; domain: (- , -10) (-10, )
x + 10
50) (q
n)(x) =
1
; domain: (- , -9) (-9, )
x+9
10