Math Analysis Test Review
Functions Review (Chapters 1- 3)
Find the symmetry of the following functions. (No symmetry, origin, x-axis, and/or y-axis.)
1. y = 2x3 – 7x
2. y = 3x2 – 5
3. x + 5y2 = 3
4. Solve by all 3 methods (inverse,
Cramer’s, and RREF).
5. Find the domain of
9x
.
f ( x)  2
x  17 x  42
6. Find the intercepts of
3x  4
.
g ( x) 
x2
x-intercept(s):_____________
y-intercept:________________
7. Find the average rate of change
of f(x) = x2 + 3
from 1 to 5.
8. Given
45, if 0  x  225
h( x)  
0.13x  30, if x  225
find h(248).
9. If j ( x) 
3x
, find
x 4
2
a) j(-7)
a)_________
b) j(2x)
b)_________
If f(x) = 2x2 – 3x + 5 and g(x) = x + 3, find simplified expressions for the following.
10. f(x) + 7
11. f(x + 2)
12. – f(x)
13. g – 1
14. f ○ g
15. g ○ f
Determine if the following functions are even, odd, or neither algebraically.
16. f(x) = 4x3 – 5x + 2
2x
17. g ( x)  2
x 3
2
5x  4
and g ( x) 
, find the following. Please state the domain of each.
x 1
x 8
18. f + g
f
19.
g
If f ( x) 
20. f
–1
21. f ○ g
Graph the following functions. State the domain and range.
22. f(x) = |2x| – 7
23. g ( x)  7  x
Domain:____________ Range:______________
Domain:____________ Range:______________
Graph the following functions. State the domain and range.
3x  4, x  2
24. f ( x)  33 x  4  6

x  2
25. g ( x)  5,
 x  1, x  2

Domain:____________ Range:______________
Domain:____________ Range:______________
26. Given the graph of h(x), find the following:
a) the domain of h(x)
b) the range of h(x)
c) h(7)
d) the value(s) of x for which h(x) = -2
e) the number of times the graph of y = 3 intersects
the graph of h(x)
f) the x-intercept(s)
g) the y-intercept
h) the increasing intervals
i) the decreasing intervals
j) the intervals when h(x) > 0
k) the local maxima
l) the graph of 2∙h(x + 1)
m) the graph of h(2x) – 5
27. Find the equation of the quadratic function that
has a vertex at (-2, 6) and contains the point
(-4, -2).
28. A farmer with 2000 meters of fencing wants to
enclose a rectangular plot for planting that borders a
straight highway. If the farmer does not fence the
side along the highway, what is the largest area of
the field?
29. Determine if the function is a polynomial, and
state the degree if it is a polynomial.
a) f ( x)  1 
1
x
2
b) g ( x)  3 
1
4x
30. Form a polynomial that satisfies the following:
Zeros: -2, multiplicity 2; 3, multiplicity 1
31. Given f(x) = (x – 2)2(x + 2)(x + 4), find the …
32. Given g(x) = x2(x2 + 1)(x + 4), find the …
a) intercepts:
a) intercepts:
b) whether the graph crosses or touches the x-axis at
the zeros:
b) whether the graph crosses or touches the x-axis at
the zeros:
c) end behavior:
c) end behavior:
d) maximum number of turning points:
d) maximum number of turning points:
e) intervals on which the graph is above or below the
x-axis:
e) intervals on which the graph is above or below the
x-axis:
f) sketch using the information in parts a-e.
f) sketch using the information in parts a-e.
33. Find the domain and range of
x 2  x  12
f ( x)  2
.
3x  5 x  8
34. Find the domain and range of
x2  2x  8
g ( x)  2
.
4x  5x  6
Domain:______________________
Domain:______________________
Range:_______________________
Range:_______________________
35. Find the vertical, horizontal, and/or oblique
2 x 2  5x  3
asymptote(s) for H ( x) 
, if any.
x4
36. Find a rational function that might have the
graph shown below.
Vertical Asymptote(s):________________
Horizontal Asymptote:________________
Oblique Asymptotes:_________________
37. Analyze the function, and sketch the graph of
x 2  3x 10
.
Q( x)  2
x  8x  15
38. Analyze the function, and sketch the graph of
x 2  x  12
.
R( x) 
x2  4
Domain:__________
Intercepts:_________
Symmetry:_________
Asymptote(s):_______
Intervals above x-axis:_______
Intervals below x-axis:_______
Domain:__________
Intercepts:_________
Symmetry:_________
Asymptote(s):_______
Intervals above x-axis:_______
Intervals below x-axis:_______