Math 3
CHAPTER 2 TEST
Name:_______________________________________________
On the first graph, draw a relation that is a function but not one-to-one. On the second graph, draw a one-to-one
function. Make both graphs continuous.
1)
*Determine whether the relation is a function. Explain your answer choice. Find and identify the domain and range.
2) {(1, -3), (-1, -6), (4, -3), (8, 5), (12, 9), (0, -5)}
Yes this is a function because each x-value has a unique y-value.
D: -1, 0, 1 , 4, 8, 12
R:
-3, -6, 9, -5, 5
*Determine whether the equation defines y as a function of x. If it is a function, determine whether it is one -to-one.
x+1
3) y =
x2
Yes, y is a function of x and the function is not one-to-one.
*Determine whether the function is one-to-one. Explain how you determined your answer.
4) f = {(6, 7), (-9, -4), -4, 8 , 0, 5 , (18, 13)}
yes, it is one-to-one because each y-value has a unique x-value.
Find the inverse of the function. Find and identify the domain and range of the f(x). (10 points)
x+7
5) f(x) =
2-x
y=
x+7
2-x
x=
y+7
2-y
x2-y =y+7
2x - xy = y + 7
y + xy = 2x - 7
y 1 + x =2x - 7
2x - 7
y=
1+x
2x - 7
f-1 x = =
1+x
Domain: (
, 2) U ( 2, )
1
Find the difference quotient for the function and simplify it.
6) f(x) = 6x 2 - x - 7
f(x + h) = 6 x + h 2 - x + h - 7 = 6 x2 + 2xh + h 2 - x - h - 7 = 6x 2 + 12xh + 6h 2 - x - h - 7
6x 2 + 12xh + 6h 2 - x - h - 7 - 6x2 - x - 7
12xh + 6h 2 - h
=
= 12x + 6h - 1
h
h
*Evaluate.
7) Find (f
(f
g)(-3) given f(x) = 4x2 + 2 and g =
2, 5 , - 1, -3 , 3, 0 , - 3, -5 , -4, -6
g)(-3) = f g - 3 = f - 5 = 4 - 5 2 + 2 = 4(25) + 2 = 100 + 2 = 102
*Find the indicated function.
8) Let f = (-2, 3), (-1, -3), 1, - 7 , (6, -9), - 9, 4
Find f · g, and g f.
f · g (- 2, - 27), (6, 63)
g
and g =
3, -2 , (-2, -9), - 3, 0 , (4, 1), (6, -7)
.
f (-2, -2), (-1, 0), - 9, 1
*Find the requested function value.
9) Find (f g)(x) when f(x) = 9x - 3 and g(x) = - 6x + 7.
(f
g)(x) = f g x = f - 6x + 7 = 9 - 6x + 7 - 3 = - 54x + 63 - 3 = - 54x + 60
Solve the problem.
10) If f varies jointly as q and the square of h, and inversely as the square root of w. If f = 36 when q = 3, h = 2
and w = 5, find f when h = 4 q = 3, and w = 60.
f=
kqh 2
w
36 =
k3 22
5
36 5 = 3k 4
36 5 = 12k
3 5=k
f=
3 5 3 42
60
=
5 9 16
2 15
=
98
3
=
98
3
·
3
3
=
72 3
=24 3
3
Write the equation of the graph after the indicated transformation(s).
11) The graph of y = x2 is vertically stretched by a factor of 5, shifted 7 units to the left, 8 units upward, and the
resulting graph is reflected across the x-axis.
y = - 5(x + 7) 2 + 8
2
Determine algebraically whether the function is even, odd, or neither.
12) f(x) = 9x 4 - 8 x - 9
f(- x) = 9 - x 4 - 8 - x - 9
f(- x) = 9x 4 - 8 x - 9
this is an even function
*Decide algebraically whether or not the functions are inverses of each other.
13) f(x) = 6 - x , g(x) = 6 - x 2
(f
g)(x) = f g x = f 6 - x 2 =
6 - (6 - x 2 ) =
x2 = x not inverses
this is the graph of f & g.
Draw a graph of a continuous function that is increasing on the interval (- , -3), decreasing on the intervals -3, 2 &
8, , and constant on the interval 2, 8
14)
3
Graph the basic function, and the given function using transformations. Use a dashed line to show any intermediate
transformations. Use a solid line for g(x) and the basic function. Label all phases of the graphing process that are
illustrated. USE ACCURATE POINTS ONLY.
1
x+3 -5
15) g(x) = 4
g(x) =g(x) = x is the solid graph at the origin (green)
1
g(x) =
x is blue
4
g(x) =
1
- x is red
4
g(x) =-
1
x + 3 - 5 is black
4
Graph the function. USE ACCURATE POINTS ONLY. (10 POINTS)
16)
1 2
x -9
2
f(x) =
for x
-3
2 x+3 +1
for - 3 < x < 3
- x - 1 for x 3
4
1
x+3 -5
4
the left side of the step functions should have solid dots and the right side open circles. The computer will not
allow me to add more points.
5