A2A Practice Exam 3: Be aware that the following problems are not inclusive but just examples of the content listed
above. Go over the homework sets for further examples. Correct the problems on the hw that you got wrong. The
following problems are designed to match the exam 3 content.
 b  b 2  4ac
Quadratic Formula:
2a
b
2a
Vertex:
An equation and its graph are given.
A) Use the graph to determine whether the graph is symmetric with respect to y-axis(even), x-axis, origin(odd), or it has
no symmetry.
B) Determine algebraically if functions 1-4 are even, odd or neither. Your answer should match what you deduce from
the graph.
Algebraic model: ODD:  f ( x)  f ( x) EVEN: f ( x)  f ( x)
Example:
1.
2.
f x   2 x 6  2 x 2  1

f ( x)  2( x) 6  2( x) 2  1 hence function would be even
f ( x)  x 4  2 x 2  1
y
3.
g x   x3  x
4.
x  y2
3
x 3
2
5. What is the domain and range of the above graphs? Write your answer in interval notation
6. Rewrite the equation 2x + 3y = 5y – 8 using function notation
7. Complete the following table
X
-2
-1
0
1
2
3
f x   3x  1
2
8. A farmer has a rectangular garden plot surrounded by 344 feet of fencing. Find the dimensions of the garden if its
area is 7227 ft2.
9. The graph to the right is a graph of h(x).
a. Find h(3); h(-1); if h(x) = 4 find x; if h(x) = -3 find x.
b. Find the domain and range of h(x)
10. For each of the following representations of a relation, state whether the relation is or is not a function. Explain your
answer.
h(x)
s(t)
x
-2
-1
0
1
2
y
3
2
1
2
3
(-2, -3), (-1, -2), (0, -1), (-1, 0), (-2,1)
11. What is the domain and range of h(x), f(x) and g(x) below? Write your answers in interval notation and in set
notation.
f(x)
g(x)
h(x)
fx = x3+2
hy = y2-2
4
4
2
2
-5
-5
5
5
-2
-2
-4
-4
12. Using the above graphs of f(x), g(x) and h(x) above
a.
Find f(-2), f(2), g(0), g(1), h(-3), h(-1), h(1)
b.
Find x if g(x) = 2, f(x) = -2, f(x) = 0, g(x) = 1, h(x) = -2
13. Given the function g ( x)  3x 2  4 x
a. Find
g ( x  h)  g ( x )
h
b. Find g ( x  2 )
14. Graph the following functions using transformations. Be able to list the transformations (in words) that you applied to
each expression.
3 x4 5
3  2( x  1)2
4 3 x
15. Given the graph on the right find the equation for base graph f(x) (blue) and the
transformations applied to create g(x) (maroon).
16. Given y  2 f ( x  1)  4 , describe in words how the graph of f(x) has been transformed to create y.
17. Given the graph of h(x) to the right, draw y  2 f ( x  3)  2
18. The collision impact of an automobile varies jointly as its mass and the square of its speed. Suppose a 2000lb car
traveling at 55 miles per hour has a collision impact of 6.1. What is the collision impact of the same car at 65 miles
per hour?
19. a)
b)
c)
d)
Given the piecewise graph of f(x) to the right, find f(-2) and f(2)
Find the domain of f(x)
Determine the domain and range of f(x) in interval notation
Describe f(x) as a function
if
 3
 x  2
if
20. Given the piecewise function g ( x)  
2
 x  1 if
 3
x  2
2 x3
find g(0), g(-5), g(2), g(3). Graph g(x) using
x3
transformations and the given domain restrictions.
21. Find the domain and range of the following functions. Which functions have domain restrictions?
f ( x)  2 x 3  3 x 2  5
g ( x)  2 x  1
22. Use the following functions to answer a – i.
a.
b.
c.
d.
e.
f.
g.
h.
i.
h( x ) 
2x
x 4
m( x ) 
2
g ( x)  1  x
h( x ) 
4
x 4
Determine the domain of each function individually
Find (f + h)(x) and list the resultant domain in set notation
Find (g/f)(x) and list the resultant domain in set notation
Find ( f  h)( x) and list the resultant domain in set notation
Find ( f  h)( 3)
f ( g ( x))
h( f ( 1))
g ( f (2))
f ( x  3) * 2 f ( x)
23. Given the graph on the right find where f is in maroon and g is in blue,
( f  h)( 2) , ( f  h)( 6) , ( f * h)( 3) , and ( f  f )( 4)
24. a) Given f ( x) 
3x  2
and T ( x)  2 x  6 find f -1 (x) for both functions.
4
b) State the domain and range in set notation of f(x), f -1 (x), T(x) and T -1(x)
2
x4
2x  3
f ( x)  x 2  2 x
25. Use the inverse function property of composition to determine if f ( x)  5 x  2 and g ( x) 
1
2
x  are inverses.
5
5
26. Find the inverse functions for the following functions. Write your answer in terms of f 1 ( x) :
a.
f ( x) 
3x  2
5x
b.
f ( x)  2 x 2  4 ; x  1
(Hint: Graph f(x) using functions and consider how the domain and range of f (x ) and f 1 ( x) are related.)
27. Given the graph S(t) on the right:
a) State the domain and range or S(t) in set notation.
b) Is S(t) a one-to-one function? Why.
c) Explain in words how the domain and range of S(t) is related to the domain and
range of its inverse.
d) Draw the inverse function for S(t). Is the graph one-to-one?
28. Be able to write your answer in set notation or interval notation and know the difference.
(, 2]
 {x | x  2}
(24, 15)  {x | x  R,  24  x  15}