Download Chapter 11 Review

Chapter 9 Review
Pre-calculus
Show all work. Also study your notes & quizzes for this test!!
Name: _______________________
Date: ______________Hour: _____
1. Find a formula for the function in the graph.
2. Write a formula, if f has a degree that is equal to 3 and passes through the following points:
f  6   f  5   0 and f  4   2.5
3. Find the limit as x→± infinity and real zeros for each of the polynomials.
a. f ( x)  2 x 2  11x  6
b. g ( x)   x 4  81
c. h( x)  x 3  3x 2  10 x
4. Write an equation in standard form for a polynomial with zeros at x = 6, x = 1,
x = 5 multiplicity of 2, and a y-intercept at 3.
5. Given f(1) = 2 and f(2) = 16, find the following equations using algebra. Show all work.
a) Find a power equation that passes through the two points.
b) Find an exponential equation that passes through the two points.
c) Find a linear equation that passes through the two points.
Find the following for each equation:
a) Holes
b) Vertical asymptote(s)
c) Horizontal or slant asymptote
d) Zeros
e) y-intercept
f) Is function odd, even or neither?
g) Graph the rational function
f ( x) 
6.
8. h( x) 
2 x 2  2 x  24
5 x 2  10 x  15
7. g ( x) 
3x 2  6 x  9
x7
x 8
x 2  25
9. k ( x) 
5x  2
x4
10.
If y is directly proportional to the square of x and y = 12 when x = 2, find the
constant of proportionality. __________
Find y, when x = 3. _________
11.
If y is inversely proportional to x and y = 12 when x = 2, find the
constant of proportionality. __________
Find y, when x = 3.
12.
a)
_________
Are these functions are a power function, rational function, exponential function, or none.
3  x2
___________________
b)
k ( x) 
f ( x)  3x(2 x  4) 3 ___________________
x4
c) g ( x) 
63 x
___________________
5
d) h( x)  5(7) x  2
___________________
Match the functions with the graphs given below.
y
13. f  x   3x
______________
14. g  x   ln x ______________
15. h  x   x
x
1
16. t  x   x7
3
______________
______________
17. Given the following functions, determine which function dominates as x   . Which function dominates?
a) y  5x
7
2
c) y  1000x 2
or
y  400x 3
b) y  7x 8
or
y  5(1.07) x
or
y  4x 6
d) y  20x 5
or
y  2(1.5) x
18. Write the following as ratios of two polynomials.
a) g ( x) 
1
5
x3
b) f ( x) 
2
x 1

x4 x2
19. The total cost for manufacturing Chevy Cavaliers is C  x   0.2x 3  2.3x 2  14.3x  10.2 where x is the number
of cars produced each hour and C(x) is the cost in thousands of dollars.
The average cost function: A  x  
Cx
x
a) What is the average cost, A  x  , of producing five Cavaliers per hour?
b) What is the minimum average cost, A  x  , per hour in thousands of dollars?
20. Write an equation for the rational equation graphed below.
21. Bronze is an alloy made of copper and tin. The alloy initially contains 3kg copper and 9kg tin. You add x kg
of copper to this 12kg of alloy.
a) Find the % concentration of copper in this alloy as a function of x, f(x).
b) Evaluate the following and explain the meaning in this situation.
f(½)
f(-1)
f-1(½)
f-1(0)