College Algebra TEST #2 MAT 141

PROF. PORTER STUDENT NAME:___________________________

1. What is this course all about?

Can you think of three different ways that you can describe f(x)?

2. Suppose you are trying to sell some lemonade. If you discover that 200 cups sell at 25 cents, and 500 cups sell at 10 cents, then use a linear relationship to describe the number of cups N you can sell given the price P?

(leave the equation in point -slope or slope intercept form)

Answer:_________________________

3. Suppose that you also find that you can sell 1000 cups at 5 cents. Combined with the sales figures in the problem above, find the linear regression that fits all three sales points.

Answer:_________________________

4. Given the function f(x) = 3x² - 7

Give f(a)

f(a):_________________________

Give f(a+h)

f(a+h):_________________________

Find and simplify:

Answer:_________________________

5. Sketch the graph of the function . Give the domain and range.

Domain:_________________________

Range:_________________________

6. Graph : g(x) = -2(x - 5)² + 8

Explain in words what has happened to the parabola above.

Label the x -intercepts

In the graph above, when is the graph increasing? Decreasing? A Maximum? A Minimum?

Increasing:_________________

Decreasing:______________

Maximum:_______________________________

Minimum?___________________________________________

For 8 and 9:

Given the functions below: Find:

r(t) given by the table:

t =	0	1	2	3
r =	3	2	0	1

h(t) given by the graph:

X
		X
	x
			X
				X

0 1 2 3 4 5 x

8. Find (h o r)(3).

(h o r )(3)=_________________________

What is the domain for (s + p ) (t) ?

Domain:___________________

9. Find s^-1(x)

s^-1(x) = _________________________

Find (p o p^-1)(10¹⁰⁰)

(p o p^-1)( 10¹⁰⁰)._________________________

10. Perform the operation (1 – 3i) / (5 + 7 i)

11. Solve using a graph.

12. Give the solution to the inequality as a graph, in interval notation, and as an equation: f(x) = x(x-3) (x+4) > 0