1. For the points (-1, 1) and (2, 5), find the distance d between the points and the midpoint M of the line segment which connects them.

 

 

 

 

 

 

 

2. Determine whether or not each of the following relations represents y as a function of x. Find the domain and range of those relations which are functions.
3. (-1, 1) (0, 5)  (1, 7)  (-1, 6)
4. y =

 

 

 

 

 

 

 

 

3. Find an expression for a function that takes a real number f(x) and performs the following three steps in the order given:

(1) multiply by 2   (2) subtract 4    (3) take the square root

 

 

 

4. Use the function f(x) = 3 – x ² to find
5. f(-2) b.  f( )     c.   f(a + 2)

 

 

 

 

 

 

 

 

 

 

 

5. Find the domain of f(x) =

 

 

 

 

 

 

 

 

6. Use the pair of functions f(x) =     and g(x) =     to find  (-1)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7. Find and simplify the difference quotient for the function f(x) = x² + 3.

 

 

 

 

 

 

 

 

 

 

 

 

8. The cost, in dollars, to produce x widgets is C(x) = 3x + 32 , x > 0. The price-demand function, in dollars per widget, is p(x) = 30 – x.
9. Find and interpret R(10), where R(x) is the revenue function.
10. Find and interpret P(10), where P(x) is the profit function.

 

 

Sketch the graph of the given function. State the domain of the function,

identify any intercepts and test for symmetry.

 

9. f(x) =