MAT1033 Intermediate Algebra
Practice Exam 1
Name______________________________________________
SHORT ANSWER. Show all work and box your answer (if applicable). If no work is shown, no credit will be given.
Graph the equation by determining the missing values needed to plot the ordered pairs.
1) x - 3y = -6; (0, ), ( , 0), (1, ), ( , 1)
y
10
5
-10
-5
5
10
x
-5
-10
1
1)
Find the x- and y-intercepts. Then graph the equation.
2) 5x - 30y = 30
2)
y
10
5
-10
-5
5
10
x
-5
-10
Find the midpoint of the segment with the given endpoints.
3) (3, 7) and (9, 2)
3)
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line
through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
4)
4) (2, -5) and (3, 6)
2
5) (6, -8) and (6, 7)
5)
Find the slope of the line.
6)
6)
y
10
5
-10
-5
5
10
x
-5
-10
3
Decide whether the pair of lines is parallel, perpendicular, or neither. You must show all work and prove your answer.
7) 3x - 4y = 17 and 8x + 6y = -6
7)
Find the equation in slope-intercept form of the line satisfying the conditions.
3
19
8) m = - ; y-intercept 0,
5
5
Write the equation in standard form of the line satisfying the given conditions.
2
9) Through (4, 3); m = 3
4
8)
9)
Write the equation in standard form of the line through the given points.
10) (-6, 0) and (1, 8)
10)
Find an equation of the line satisfying the conditions. Write the equation in slope -intercept form.
11) Through (-3, 8); perpendicular to -3x + 4y = -23
11)
Graph the linear inequality in two variables.
12) x + y ≤ 6
12)
y
10
5
-10
-5
5
10
x
-5
-10
5
Graph the compound inequality.
13) x + y ≥ 2 and y ≤ 2
13)
y
4
2
-4
-2
2
4
6x
-2
-4
-6
Decide whether the relation is a function.
14) {(-2, 1), (2, 2), (6, 7), (8, 3), (11, -9)}
14)
Give the domain and range of the relation.
15) {(1, 8), (-1, -8), (-7, -4), (6, 0)}
15)
6
Decide whether the relation is a function.
16)
11
-4
-17
-20
16)
Give the domain and range of the relation.
17)
17)
Decide whether the relation is a function, and give the domain and range.
18)
18)
10
y
5
-10
-5
5
x
-5
-10
7
Solve the problem.
19) Find f(-4) when f(x) = x2 - 4x - 3.
19)
Evaluate the function.
20) Find f(5) if f = {(-2, 3), (3, 0), (0, 5), (5, -2)}
20)
An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation
f(x).
21) 5x - 6y = 5
21)
8
Answer Key
Testname: MAT1033 PRACTICE EXAM 1 - S14
1)
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
2) (6, 0); (0, -1)
y
10
5
-10
-5
-5
-10
3) 6,
9
2
4) 11; rises
5) Undefined; vertical
3
6) 4
7) Perpendicular
3
19
8) y = - x +
5
5
9) 2x + 3y = 17
10) 8x - 7y = -48
4
11) y = - x + 4
3
9
Answer Key
Testname: MAT1033 PRACTICE EXAM 1 - S14
12)
y
10
5
-10
-5
5
10
x
-5
-10
13)
y
4
2
-4
-2
2
4
6x
-2
-4
-6
14) Function
15) Domain: {-7, -1, 1, 6}; Range: {-8, -4, 0, 8}
16) Function
17) Domain: {4, 7, 12}; Range: {5, 8, 13}
18) Function; domain: (-∞, ∞); range: [2, ∞)
19) 29
20) -2
5 - 5x
21) f(x) =
-6
10