Algebra 2
Review – Unit 5/Ch.7 - Radical and Rational Functions
Name _________________________________
Simplify each radical expression.
49x 2 y10
1.
4.
3
12  36
3
8. (7 
3
2.
5.
64 y 9
3.
56 y 5
6.
3 7y
7 x  14 x
9.
3
3
3
6)(7  6)
32x 9 y 5
7.
27  75  12
10. ( 5 
81a8b5
3
3a 2b
6)2
Simplify each expression. (Rationalize the denominator)
11.
2
12.
1 5
x
2
13.
5
3x
Simplify each expression. Assume that all variables are positive.
14. x
1/6
 x 2/3
15.
( x 3/8 y1/4 )16
16. 36
3/2
17.
(
27 x 9 y12 2 / 3
)
8x3 y 3
Find the inverse function. Is the inverse a function?
18. y 
x2
19.
f ( x )  2.4 x 2  1
20.
y  x3  1
Solve each equation. Check for extraneous solutions.
21.
x3 5  x
22.
(3x  4)1/3  5
23.
3
3x  1  5
Graph each function. Write the list of transformations. Find the domain and range of each function.
Make your points clear so that I can see that you understand the process!!!
24.
y = √(x + 4) + 2
25.
x
y   x 1  4
x
y
26. The time t in seconds for a swinging pendulum to complete one full cycle is given by the function
t  0.2 p , where p is
the length of the pendulum in cm. If it takes the pendulum 0.9 seconds to make a full cycle, what was the length of the
pendulum?
Let f ( x )  2 x  5 and g(x) = x2 - 3x. Perform each function operation.
27. ( f  g )( x )
28. f ( x )  g ( x )
29. g ( x )  f ( x )
y
30.
g ( x)
f ( x)
For each pair of functions…
31. Find
f ( g ( x ))
f ( x)  x 2 , g ( x)  4 x  1
32. Find
g ( f ( x))
f ( x)  2 x 2  x  7, g ( x )  3x  1
f ( x )  x 2 and g ( x )  x  3 . Evaluate each expression.
33. ( g f )( 2)
34. ( f g )( 2)
Let
38. Graph the parabola.
y  ( x  1) 2  3
35. ( f
Factor:
39. x  10 x  25
2
40. 25 x  36
2
41. 6 x  7 x  2
2
g )(0)