Algebra II 2nd Semester Practice Final
Name: ___________________________
1.) Find (f + g)(x) for f(x) = x + 8 and g(x) = 3x.
2.) Find (f – g)(x) for f(x) = x2 + 2x and g(x) = 5x + 1.
2
3.) Find (f • g)(x) for f(x) = 4x and g(x) = 3 – x.
4.) If f(x) = 2x + 4 and g(x) = 6x – 7, find g[f(-5)].
2
5.) If f(x) = 3x and g(x) = 2x – 8, find [g ○ f](x).
6.) Graph the equation
√
. State the domain and the range.
7.) Find the inverse of f(x) = 3x – 5.
8.) Sketch the graph of
√
(get a sheet of graph paper)
9.) Write the radical √
using rational exponents.
10.) Solve the equation (
)
11.) Solve √
12.) If
, then x = ?
13.) Find the domain and range of the function
( )
14.) Give an example of a function with exponential growth? __________________
Give an example of a function with exponential decay? ___________________
15.) Solve
16.) Write the equation
in logarithmic form.
17.) Evaluate
18.) Solve
19.) Solve
(
)
(
)
20.) Solve
21.) Solve
22.) Express
. Round to the nearest ten-thousandth.
in terms of common logarithms.
23.) Suppose you deposit $15000 in an account paying 4% annual interest, compounded continuously.
Use
to find the balance after 20 years.
24.) Solve
25.) For what value(s) of x is the expression
Simplify:
26.)
27.)
28.)
29.)
undefined?
30.) Find the LCM of 4x + 8, and 8x+16
31.) Determine the equations of any vertical asymptotes of the graph of
( )
32.) Determine the values of x for any points of discontinuity in the graph of
( )
33.) If y varies directly as x and y = 15 when x = -3, find y when x = 8.
34.) If y varies inversely as x and y = 3 when x = 7, find y when x = 42.
35.) Solve
36.) Solve
37.) Write the equation of the parabola y = 3x2 – 6x + 2 in standard form.
38.) Write an equation for the parabola with focus (2, 4) and vertex (0, 4).
39.) Graph the equation
40.) Write an equation for a circle if the endpoints of a diameter are at (-3, 6) and (7, 6).
41.) Write the equation of a circle with center (0, 2) and radius 9 units?
42.) Write the equation of an ellipse with foci at (0, 2) and (0, -2) that has
the endpoints of its major axis at (0, 3) and (0, -3)?
43.) Graph the equation:
. What type of conic section is it?
44.) Write the equation of a hyperbola with vertices (0, 5) and (0, -5) and foci (0, 7) and (0, -7)?
45.) Graph the equation:
46.) Find the 30th term of the arithmetic sequence in which a1 = 2 and d = 9.
47.) Write an equation for the nth term of the arithmetic sequence: -1, 2, 5, 8, …
48.) Find two arithmetic means between 6 and 30.
49.) Find the seventh term of the geometric sequence for which a1 = 5 and r =4 .
50.) Write an equation for the nth term of the geometric sequence -20, 5,
,…
5
51.) Find:
∑
n=1
52.) Expand (x + 4y)5.
53.) Use the Binomial Theorem to find the third term in the expansion of (x + 4y)7.