Integrated Trigonometry – Spring Midterm Review
Name
1. Graph each of the following:
1
3
1
3
b. y  x  3
a. y  3 x  2
2. Graph the following piecewise function:
c. y   x  1
d. y  3 x  1

3
if x  2

f  x   2 x  3 if  2  x  0
1
 x 2  1 if x  0
2
 x  3 if x  0

f ( x)  3 - x if 1  x  3
3x if x  3

3. Find the domain of the function:
a. f  x  
5
x3
b. f  x  
x 3
x 2  2 x  15
c. f  x   x  4
1
x
1
c. f  x   
x 3
4. Describe the transformations of the function from the parent graph of f  x  
a. f  x  
1
4
x 7
b. f  x  
4
x
5
.
d. f  x   
6
.
7. Find the exact roots of the polynomial.
a. x3  7 x2  10x  0
b. x2  100  0
f. x 2  18  0
e. x3  9x  0
c. x 4  10 x 2  9  0
d. x2 121  0
g. x 4  x 2  2  0
h. x 3  4 x 2  5 x  20  0
8. Write the polynomial equation of least degree for the roots given.
a. 1,0,-5
b. -2,  4i
c. 8 (M=2), 3i , 0
9. Divide.
a. ( x 3  4 x 2  5 x  11)  ( x  1)
10.
3
7
x 2
b.
(2 x 4  3x  1)  ( x  3)
Find the remainder for each division. Is the divisor a factor of the polynomial?
( x 3  7 x 2  16 x  112)  ( x  4)
a. ( x 3  4 x 2  100)  ( x  5)
b.
R
Factor?
R
Factor?
11. Find all possible rational zeros of the function. Then determine all the zeros.
a.
b. f ( x)  2 x 4  3x 3  8 x 2  9 x  6
f ( x)  8x 3  6 x 2  23x  6
Possible zeros:
Possible zeros:
Zeros:
Zeros:
12. Graph the following functions and find the domain, range, and find the maximum or minimum.
a. y  ( x  4)2  3
2
b. y = -3x +12x - 5
2
c. y  2x  12x  7
13. Write the equation to the following graph. (Hint: use the x-intercepts to write the equation)
14. Write the interval of increase, decrease, end behavior, maximum(s), and minimum(s) for each graph below.
a.
b.
c. (approximate as best as you can)
15. Find the zeros
a. y  2x2  12x  7
b. y  x( x  2)( x  7)
c. y  3x3  21x2  36x
16. Graph the following functions and find the vertical asymptote(s), horizontal asymptote(s), and holes.
a. y 
17. Solve
x3
2
x  21x  54
b. y 
2x  5 4x  1
3x  8

 2
.
x
x2
x  2x
x2  6 x  3
x 2  5 x  24
18. Solving each rational equations/inequality.
x 1
8
3x
5
a.
b.

9

x 1 x 1
4x
x 1
c.
4x
 8 (express final answer in interval notation)
3x  8
19. Write the equation of the following lines:
a. Write the linear equation of a line with a slope of 3 and passing through the point (3, -5).
b. Write the linear equation that contains the points (-5, 4) and (-6, 0).
c. Write the linear equation that is perpendicular to y = 4x – 9 and through the point (5, 3).
20. Simplify each expression. State domain restrictions when appropriate.
a.
b.
c.
d.
e.
f.
g.
h.
21. Write the equation of the rational function with the given characteristics.
a. VA @ x = 1, HA @ y = 0, no holes, no x-intercepts
b. VA @ x = -1 and x = -3, HA @ y = -2, x – intercepts @ x = 3 and x =2
c.
22. Solve the following word problems.
d. Same graph as in part (c) but with a hole at x = 0