Pre-Calculus: Chapter 1 Review
No Calculators
1. As an employee in sales, you receive a monthly
salary of $1800 plus a commission of 4% of your
sales. Write an equation expressing the monthly
wages y in terms of sales x. If you receive $3700
in wages for the month of January, what were
your sales for that month?
Name: ________________
2. A rectangle of length x and width w has a
perimeter of 60 meters.
a) Draw a diagram
b) Write the function for Area in terms of x.
c) What is the domain of the function?
3. Determine the equation of the line that passes
through the point (4, -5) and is perpendicular to
3
y   x7.
5
4. Find the difference quotient and simplify your
answer: f ( x)  5x 2  2 x  1
5. Determine algebraically if the function is even,
6. Use the algebraic tests to check for symmetry with
respect to both axes and the origin.
y  6  x3
odd, or neither.
f ( x)  2 x x  3
2
f (3  h)  f (3)
,h  0
h
7. Write an equation for the following function:
8. List the transformations in order and graph.
f ( x)   x  1  4
9. List the transformations in order and graph.
3
h( x )  2   x   3
10. Graph the piecewise function
 x  2, x  2

h( x)   x 2  1,  2  x  1
 4  2 x,
x 1

11. Describe the intervals on which the function is
increasing, decreasing, or constant.
1
2x  5
12. Find f ( x) if f ( x) 
7x 1
x
1
7
13. Find the average rate of change from x1 to x2 .
f ( x)   x 2  3x  5
x1  2 x2  5
15. Given f ( x)  x 2  9 and g ( x)  9  x 2
a) Find the domain of f
b) Find the domain of g
c) Find f ( g( x))
14. Find two pairs of functions f and g such that
3
f ( g ( x))  h( x) if h( x) 
(2 x  1)3
16. The weekly cost C of producing x units in a
manufacturing process is given by
C ( x)  60 x  750 .
The number of units x produced in t hours is given
by x(t )  50t , 0  t  40 where t is the time in
hours.
a) Find the composition C  x  t  
b) Interpret the meaning of C  x  t   in
context of the problem.
d) Find the domain of f ( g( x))
c) Find the weekly cost after 24 hours.
d) Find the time when the weekly cost
exceeds $15,000.