Chapter 4 Review Worksheet #1
1) F is a linear function for which F(4)=6 and F(-3)=5. Find the equation for the function F. Find F(12)
2) Does the function g ( x)  17  6 x  x 2 have a maximum or a minimum value? What is that value?
Problems 3 – 4: Convert the equation into standard form for a parabola. Find the vertex, x and y intercepts, the
axis of symmetry. For what input does the function have a maximum or minimum? What is the maximum or
minimum value? Graph the function.
3) f ( x)  5 x 2  20 x  3
4) f ( x)  6 x 2  12 x  9
5) Let f ( x)  ( x  3)2 ( x  4)5 . Find the x and y intercepts, graph the excluded regions and sketch the graph of f.
(hint: use a sign chart to find excluded regions)
Problems 6 -8: Find the x and y intercepts, and vertical and horizontal asymptotes and graph f.
Does the graph cross the horizontal asymptote? What is the behavior or graph to the left and right of vertical
asymptotes.
2x  3
1
x(2 x  1)
6) f ( x) 
7) y 
8) f ( x) 
2
x5
( x  5)( x  5)
 x  3
9) A factory owner buys a new machine for $12000. After 8 years the machine has a salvage value of $350.
Assuming linear depreciation, find a formula for the value of the machine after t years, where 0  t  8 .
Problems 10 and 11: Find real numbers, if any, that are fixed points of the given functions.
3x  1
10) f ( x)  2 x 2  8
11) g ( x) 
x 5
12) The sum of two numbers is 10. Express the difference of the squares of the two numbers as a function of a
single variable. Simplify your equation.
13) Express the distance from the point (0,2) to the point (x,y) on the parabola y  x 2 as a function of x.
Simplify your equation.
14) A farmer has a rectangular field. He wishes to fence the field and add an additional 2 lines of fencing
parallel to both sides to divide the field into 4 adjacent corrals. Suppose that you have 5000 ft of fencing to
build the corrals. Find the dimensions so that the total enclosed area is as large as possible.
1
x  24 relates the selling price p of an item to the quantity sold, x. (p is
6
in dollars). What is the maximum revenue? What price p generates this maximum revenue?
(hint: R(X) = p(x) x)
15) Suppose that the function p ( x) 