Exam Review

Functions

100

What is the domain of the function 1/x

(-inf, 0) U (0,inf)

200

What is the range of the function (x - 4)² - 3

(-3, inf)

300

Assume f(x) = 3x² + 4

find f(-3)

f(-3) = 31

400

What is the vertical asymptote

f(x) = (x² - x - 6)/(x-3)

x = 3

500

Find the x and y-intercepts

f(x) = (x² - x - 6)/(x-3)

x: (-2,0)

y: (0,2)

Expressions

100

Simplify

(3xy-15y)/(6xy-12y)

(x-5)/(2(x+2))

200

Perform the indicated operation and simplify as much as possible

6/x + 7/(5x²)

(30x+7)/5x²

300

Let g(x) = x/(x-4) and h(x) = -1/(x+2)

solve g(x) = h(x)

x = -4, 1

400

Solve for x

7x² + 12x -27 = 0 

x = -3, x = 9/7

500

Solve for x 

4/(x-3) = 9/(x+2)

x = 7

Circle

100

What is the radius of the circle equation: (x - 4)² + (y - 6)² = 81

9

200

Find the radius of a circle given the equation (x -7)² + (y + 4)² and contains the point (7, 2)

6

300

Write an equation of a circle with a radius of 13 and center is at (6, 4)

(x + 6)² + (y + 4)² = 13²

400

Find the area of a sector cut out of a circle of radius of 3 by an angle of 45^o

9pi/8

500

Find the arc length of a circle of a diameter of 9 and angle of 120^o

3pi

Angles

100

convert 135^o to radians

3pi/4

200

What is tangent in terms of the sides of a triangle relative to the angle?

opposite/adjacent

300

Find the arc length of a circle of radius 3 cut out by an angle of pi/6 radians

pi/2

400

A 10-foot ladder makes is leaned up against a wall. The ladder makes an angle of pi/4 with the ground what is the length of the wall to the bottom of the ladder?

7.07 ft

500

A right triangle ABC angle B is 25^o. The hypontonuse of the triangle AB is 10ft. What is the length of CB?

9.063 ft