Download Ata glance (MsWord)

Functional Analysis
Final Exam Review – NON Trig Review
Name: __________________________
Date: _____________ Period: _______
Unit 1 (Prerequisite)
1. Express in interval notation a. 5  x  7 3  x
2. Formula for average rate of change
3. Sketch and label a graph for the following situations
a. A function is increasing at an increasing rate
b. A function is increasing at a decreasing rate
c. A function is increasing at a constant rate
d. A function that increases on (, 3)  (2, ) and decreases on (-3,2).
e. A function that is concave up (, 2)  (2, ) and concave down (-2,2)
f.
Graph y  x 2  4 x . Give the intervals where the function is increasing,
decreasing, concave up, and concave down. Is the function bounded? Vertex?
a.
b.
c.
d.
e.
What is the equation for the average rate of change formula?
What is the equation slope intercept form of a linear equation?
What is the point slope form of a linear equation
How are the slopes related when two lines are parallel? Perpendicular?
Absolute value equations, inequalities, graphs
4.
Unit 2
1. Write the exponential function equation. What does A represent? What does B represent? From the
equation how can you tell if the function is increasing? Decreasing?
2. What do negative exponents mean? Fractional?
3. What is the formula for putting exponential equations in logarithmic form?
4. How do you solve exponential equations?
5. What are the log properties? Expanding and or condensing logs… Expanding and or condensing
6. How can you evaluate a logarithm on your calculator with a base, which is not 10 or e?
7. What is the formula for putting logarithmic equations in exponential form?
8. How do you solve logarithmic equations?
9. What is the compound Interest formula? Label what each variable stands for.
10. What is the continuous Interest formula? Label what each variable stands for.
11. Solve:
log106
1000log5
log log10
a. log 10
b. log 2 16  x
log5 15
c. 32 x  23
23 x 1  32
d. 20  12 b2
9b
 23
 45
log5 x  log5 3  log5 2
 
1 x2
3
 81
4 x  3x
log5 x  log( x  1)  2
32 x 1  3 81
3(2 x )  17
Unit 3
1. Describe how you would factor using the gcf, difference of squares, sum of cubes, difference of
cubes, perfect squares, and ordinary factoring of a trinomial.
2. Factor Completely (3) 4 x 2  36
x3  64 y 3
14m4 (m  1)  28m3 (m  1)  7m2 (m  1)
3. What is a power function?
4. Given an example of a power function with a positive exponent, negative exponent, and a fractional
exponent.
5. What is a polynomial function?
6.
7.
8.
9.
10.
11.
12.
13.
14.
How can you tell the degree of a polynomial function?
What is the standard form of a polynomial function?
Which of our 16 granddaddy functions are polynomial functions?
Write a third degree polynomial with two terms.
What is synthetic division?
Find the factors using synthetic division. f ( x)  2 x3  x 2  13x  6
How can you do long division?
Divide using long division (2 x3  10 x 2  16 x  96)  ( x  4)
If the zeros of a polynomial function are 4, -1 and a double root of x, write the equation and sketch
the graph
15. Suppose f (1)  34 and f (2)  48
Find a. a linear function, exponential function, and a
power function
16. Sketch: y 
1
x5
1
y   x5
y  x5
y  x6
1
y  x 6
y  x6
17. In a rational function how do you find the EBM, x intercepts, y intercepts, holes, vertical asymptotes,
horizontal asymptotes, and slant asymptotes
18. Give the information from # 19 above and graph
y
( x  1)
.
2
( x  x  6)
y
19. Writing the equation from a graph
( x  1)
2
( x  x  6)
y
( x 2  x  6)
( x  1)
y
(4)
( x  2)
( x  x  6)
2