Final Exam Review

Exam 1

100

(7.1 x 10⁶)/(8.2 x 10¹)

8.659 x 10⁴

200

5/(4 - rad(2))

(20 + 5 rad(2))/14

300

(x3 - x2 - 42x)/(2x2 - 20x + 42)

x(x + 6)/2(x - 3)

400

What is the equation for the line, in slope-intercept form, that is perpendicular to 4x−3y=6 through point (4,6)?

y = (-3/4)x + 9

500

Solve and write your answer in interval notation.

|2z - 7| > 1

(- infinity, 3) U (4, infinity)

Exam 2

100

Find the domain of g(w) = rad(9w+7)

[-7/9, infinity)

200

Given f(x) = x^2 + 2x and g(x) = 2x+1, what is f(g(2)).

35

300

Find the inverse 

y = 2 + rad(x - 4)

(x - 2)^2 + 4

400

The population of a city increased from 23,400 to 27,800 between 2008 and 2012. Find the change of population per year if we assume the change was constant from 2008 to 2012.

From 2008 to 2012, the city's population increased by 1100 people per year.

500

Solve for x and y. 

6x − 5y = 8

−12x + 2y= 0

(-1/3, -2)

Exam 3

100

If x varies directly as y, and x = 27 when y = 6, find x when y = 2. 

x = 9

200

Write the exponential function that passes through (1,6) and (4,48). 

y = 3 * 2^x

300

Jasmine deposits $520 into a savings account that has a 3.5% interest rate compounded monthly. What will ne the balance of Jasmine's savings account after two years?

A = 557.65

400

(2x^2+4x+16)/x^2-5x+4

Find VA

holes

HA

domain

x intercepts

VA: x = 1

HA: y = -2

holes: x = 4

domain: (- infinity, 1) U (-1,1) U (1, infinity)

x intercepts: x = -2

500

Sketch a graph of the function 

f(x) = (x-2)^2(x+3)(x - 1/2)^2

x intercepts

y intercepts

degree/# of turning points

end behavior

y int: (0,8)

x int: (4, 0) (-2, 0) (1/2, 0)

4 turning points

end behavior:

as x approaches infinity, f(x) approaches infinity

as x approaches negative infinity, f(x) approaches negative infinity

Random

100

Given f(x) = |x|, sketch a graph of h(x) = f(x-2) + 3

Leader will check

200

Find the average rate of change y = 2x^2 + x + 2; [0,1/2]

2

300

Classify as a conditional equation, an identity, or a contradiction: 

2x + 5(x - 8) = - 40 + 7x

0 = 0, identity

400

6 rad(75mp²q³)

30pqrad(3mq)

500

Solve by completing the square. 

x2 + 8x + 7 = 0

x = -7 and -1

6.7

100

log (5x) = log (2x+9)

3

200

3^x+2 = 5^x

-2log3/(log3-log5)

300

10 + ln(x+3) = 14

x = e⁴-3

400

log₇(x - 2) + log₇(x + 3) = log₇14

x = 5

500

log₄x + log₄(x - 12) = 3

x = 16