1. In exercises 1-8, we have graphed the boundary line for the linear inequality. Determine the correct half-plane in each case and complete the graph.
a. x + y <5
b. x - 2y ≥ 4
c. x ≤ -3
2. Graph each of the following inequalities.
a. x + y < 3
b. x - y ≤ 5
c. y < -4
d. 3x + 2y ≥ 0
e. 2(x + y) - x > 6
3. Business and finance. Suppose you have two part-time jobs. One is at a video store that pays $9 per hour and the other is at a convenience store that pays $8 per hour. Between the two jobs, you want to earn at least $240 per week. Write an inequality that shows the various number of hours you can work at each job.
4. Evaluate each function for the value specified.
a. f(x) = x2 - x - 2; find i. f(0), ii. f(-2), and iii. f(1)
b. f(x) = x3 - 2x2 + 5x - 2; find i. f(-3), ii. f(0), and iii. f(1).
5. Rewrite each equation as a function of x.
a. y = -3x + 2
b. 3x + 2y = 6
6. Graph the functions
a. f(x) = 3x + 7
b. f(x) = -2x + 7
c. f(x) = -x - 1
7. If f(x) = 4x-3, find the following:
f(4)
8. If f(x) = 5x-1 find the following:
f(x + 1)
9. If g(x) = -3x+2, find the following:
g(x + 2)
10. Let f(x) = 5x -2. Find a. f(4) - f(3); b. f(9) - f(8); c. f(12) - f(11).
d. How do the result of (a) through (c) compare to the slop of the line that is the graph of f?