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Mathematics 098 first test review problems
1. The graph of a relation is drawn to the right
y
(a) What is the domain of the relation?
2
1
(b) What is the range of the relation?
@
@
x
-1
(c) Is this the graph of a function?
1
2
3
2. A line L1 is known to have slope equal to 4/7
(a) what is the slope of a second line, L2 which is parallel to the first line, L1 ?
(b) what is the slope of a third line, L3 which is perpendicular to the first line, L1 ?
3. True or False: The absolute value equation |x| = −x is valid for all negative values of x.
4. If f (x) = 3x + 5, find the function value f (2).
5. If g(x) = 4x − x2 , find the function value g(−3).
6. Solve for P :
A = P rt + P
7. Suppose that the cost y (in dollars) is a linear function of the number x of items manufactured. The following information is known:
number x
0
100
cost y
1500
1550
• what is the slope of the line through these two points ?
• what does the slope measure in this situation ?
(a good answer should include units)
• find an equation for the line through these two points
8. Find an equation for the vertical line which passes through the point (3, −5).
9. Find an equation in point-slope format for the line which contains the points (14, −10)
and (68, 20).
10. Solve the absolute value inequality: |x − 55| < 2
page two
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11. Solve the linear system:
5x + 3y = 8
3x + 2y = 9
)
12. Solve the inequality: 500 − 2x ≥ x + 140
13. A bartender wants to mix a 5% alcohol solution with 25% alcohol solution to obtain
two liters of a 10% alcohol solution. How much of the weaker and how much of the stronger
alcohol solution must be mixed together?
14. Graph the equation 3x + 2y = 12.
15. Graph the linear inequality x − 2y ≥ 4.