Download Find the requested value. f(5) for f(x) = 6x + 4 if x ≤ 0 6

Quiz 2.5 - 2.6
Name___________________________________
Score ______________
Find the requested value.
1)
1)
6x + 4 if x ≤ 0
f(5) for f(x) = 6 - 4x if 0 < x < 4
x
if x ≥ 4
Graph the function.
2)
2)
10x + 2
2x2 - 5
f(x) =
if x < 0
if x ≥ 0
y
10
5
-10
-5
5
10
x
-5
-10
Give a formula for a piecewise-defined function f for the graph shown.
3)
3)
6
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
01/25/2008
Graph the equation.
4) y = x - 1
4)
y
x
Solve the problem.
5) A video rental company charges $5 per day for renting a video tape, and
then $4 per day after the first. Use the greatest integer function and write
an expression for renting a video tape for x days.
6)
Sketch a graph that depicts the amount of water in a 50-gallon tank
during the course of the described pumping operations. The tank is
initially full, and then a pump is used to take water out of the tank at a
rate of 4 gallons per minute. The pump is turned off after 5 minutes. At
that point, the pump is changed to one that will pump water into the tank.
The change takes 2 minutes and the water level is unchanged during the
switch. Then, water is pumped into the tank at a rate of 2 gallons per
minute for 3 minutes.
5)
6)
gallons
minutes
7)
Find
f
(-3) when f(x) = 4x - 6 and g(x) = 3x2 + 14x + 4.
g
2
7)
Perform the requested operation or operations.
8) f(x) = 7 - 6x, g(x) = -2x + 6
Find (f + g)(x).
9)
f(x) = 8x - 2, g(x) = 3x + 3
Find (fg)(x).
9)
10) f(x)
= 4x + 6, g(x) = 4x - 1
Find (f ∘ g)(x).
11) f(x)
=
8)
10)
x-2
, g(x) = 7x + 2
7
11)
Find (g ∘ f)(x).
Find the specified domain.
12) For f(x) = 2x - 5 and g(x) = x + 5, what is the domain of f ∘ g?
13) For
f(x) = x2 - 25 and g(x) = 2x + 3, what is the domain of f/g?
3
12)
13)
For the functions f and g, find the requested value.
14) Use the graphs of f and g to find f(3) - g(3).
5
y
5
5x
-5
5x
-5
-5
-5
y = f(x)
15) Use
y = g(x)
the graphs of f and g to find (g ∘ f)(-2).
5
-5
14)
y
-4
-3
-2
15)
y
5
4
4
3
3
2
2
1
1
-1
1
2
3
4
5 x
-5
-4
-3
-2
-1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
y = f(x)
y
2
3
4
5 x
y = g(x)
Solve the problem.
16) Regrind, Inc. regrinds used typewriter platens. The cost to buy back each
used platen is $2.10. The fixed cost to run the grinding machine is $114
per day. If the company sells the reground platens for $5.10, how many
must be reground daily to break even?
4
16)