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PM 11
Chapter 3 Review 2
1. For f (x )  x 4  3x 2  x  5 , find a) abs min b) relative max c) domain and d)
range
2. For 4 x 2  mx  3  0 , find all values of m so that one root is triple the other.
3. Solve 6x 3  7x 2  3x  0 by factoring
4. Write the equation of the cubic function with zeroes of -2, 1, and 4 and a y-intercept
of 32
5. A piece of cardboard 18cm by 12cm is used to form a box, without a top, by cutting
a square x cm from each corner.
a) Write the volume V as a function of x
b) What is the maximum volume?
c) What dimensions will give that volume?
d) What size square needs to cut for a Volume of 175cm 3
6. Sketch y = 2x – 5 and its reciprocal on the same grid. Label completely.
Determine the domain and range of the reciprocal
7. Sketch y  x 2  5 and its reciprocal on the same grid. Label completely. Determine
the domain and range of the reciprocal
Graph and label the following
8. y 
9. y 
x2
x2 3
12x
x 2 1
10. A box has a square base with sides 8cm by 8cm. and a volume of 640 cm 3 . As the
dimensions of the base change, the height changes. Let x = the change in the base and
h = the change in the height. a) Find the height b) Write h as a function of x. c) Sketch
the graph. d) by how much must the height be increased if the base in decreased
by 0.6cm? e) If the height is decreased by 2 cm by how much must the base be
increased?
11. A highway speed-trap is 1.5 km in length. The shorter the time that time through
the speed trap, the faster the car travels. Write the velocity (in km/h) in terms of the
time (in seconds)
12. Given f(x) = x 2  3x  1 and g(x) = 2x + 5, find a) f(g(-1)) b) g(f(2))
13. Given f(x) = 2x – 9, find f(x) = 0
c) f(g(x))
14. The surface area of a sphere is S  4 r 2 . Write the surface area as a function of
the diameter.
Key:
1. a) (-1.30,-8.51) b) (0.17,-4.92) c) Real numbers d) y  8.51
2. m  8
3. { 0, 1/3, - 3/2 }
10. a) h = 10 cm
b) h 
4. y = 4(x+2)(x - 1)(x – 4)
5. a) V = x( 18 – 2x)( 12 – 2x)
b) 228.16cm3
c) 2.35 cm by 13.30 cm by 7.30 cm
d) 1.15 cm or 3.78 cm
6.
640
8  x 
2
 10
c)
d) 1.69 cm
e) 0.94 cm
7.
11. v 
5400
,t  0
t
12. a) 19 b) 27 c) 4 x 2  26 x  41
13. 4.5
8.
9.
14. S   d 2