Exponential, Quadratic, Linear and Cubic Oh My!
IMP IV: World of Functions
Name:__________________
Date: _________ Period: ___
1. Solve for the indicated variable: a. x
2
– 144 = 0 b. 18 x
2
+ 3 x = 1 e. 10 = 5 e
5 x f. ln40.5 = ln e
0.21
x c. 6
3 x g.
= 81
 x
6.2
d. 4 = log x
19.5

6.2
h. A

P

1
 r n
 nt
…solve for t
2. Sketch a graph of the given functions indicating the vertex, slope, accurate x and y intercepts, and horizontal asymptotes (all when appropriate). Indicate the domain and range for each function. Indicate over what intervals the functions are increasing and decreasing. Indicate over what intervals the functions are concave up and concave down (when appropriate).You may use a calculator to check only… a. y
 
1
4 x
2 
2 x

4 b. 2 x + 3 y = 12 c. y = x
2
+ 2 x + 9 d. y = 20 e
x e. y = 100( ½ ) x f. y = (2) x +3 g. y = 10 e
2 x
+ 2 h. y

3

4 2 y

1
3. Write the standard form of the equation of a line (see 2b for an example) that is parallel to y = 4 x – 8 and passes through (-2,1).
4. Toughie…Find the distance from the line y = 9 x – 3 to the point at (-3,2). Recall from Schnorchard how the distance from a point to a line is defined.
5. Suppose v ( t ) = t
2
– 2 t gives the velocity, in ft/sec, of an object at time t , in seconds. a.) Evaluate and interpret v (0). b.) Evaluate and interpret the value(s) when v ( t ) = 0 c.) What is the meaning of the quantity v (3)? What are its units?
6. If c + d = 12 and c 2 – d 2 = 48, then what is the value of ( c – d )?
7. The tables below represent the relationship between the button number, N , which you push, and the snack, S , delivered by three different vending machines.
Vending Machine #1
N
1
2
3
4
5
6
S m&m’s pretzels
Snickers dried fruit
Hershey’s fat free cookies (Yuck)
Vending Machine #2
N
1
2
S m&m’s or dried fruit pretzels or Hershey’s
3
Vending Machine #3
N
1
2
3
4
Snickers or fat free cookies 5
6
7
8
9
S m&m’s m&m’s pretzels dried fruit
Hershey’s
Hershey’s fat free cookies
Snickers
Snickers a) One of these vending machines is not a good one because S is not a function of N. Which one?Explain why this is a bad machine to use. b) For which vending machine(s) is S a function of N ? Explain why this makes them user friendly. c) For which of the vending machines is N not a function of S ? What does this mean to the user of the vending machine?