Algebra II Review (w200)

x and y Intercepts

100

Determine the x-intercept and the y-intercept. 

y = 2x + 3

x-intercept: x= -3/2

y-intercept: y= 3

200

Determine the x-intercept and y-intercept of the line that passes through (2, 6) and (-3, -4).

x-intercept: x= -1

y-intercept: y= 2

300

Determine the x-intercept and y-intercept of the line that passes through the points (4, 21) and (7, 12).

x-intercept: x = 11

y-intercept: y = 33

400

Find the x-intercept(s) and y-intercept(s).

y = x² +2x -3

x-intercepts: x= -3, 1

y-intercept: y= -3

500

Determine the x-intercept(s) and y-intercept(s).

y = e^x -4

x-intercept: x = ln4

y-intercept: y = -3

Evaluating Functions

100

For the function f defined by f(x) = x² - 3x, evaluate f(-2).

f(-2) = 10

200

For the function f defined by f(x) = 3x² - 4x +5, evaluate f(5).

f(5) = 60

300

For the function g defined by g(x) = 2x³ -6x², evaluate g(5a).

g(5a)= 250a³ - 150a²

400

For the function f defined by f(x) = 4x² + 3x +2, evaluate f(b+1).

f(b+1) = 4b² + 11b + 9

500

for the function f defined by f(x) = x² - 3x, evaluate (f(x+Δx) - f(x))/(Δx).

2x + Δx - 3

Exponential Functions

100

Simplify using properties. 

ln(13/5)

ln13 - ln5

200

Simplify using properties.

ln√(7x)

(1/2)ln7 + (1/2)lnx

300

Simplify using properties. 

ln(x³/(√ (x²+3))

3lnx - (1/2)ln(x² +3)

400

Solve the equation.

8 = e^x+1

x = ln8 - 1

500

Solve the equation.

ln(2x - 3) = 5

x= (e⁵ + 3)/2

Parallel/Perpendicular Lines

100

Determine the slope of any line perpendicular to 

y= (1/2)x+(1/2).

-2

200

Determine the equation of the line parallel to 

y = 3x +5 at the point (4, 2).

y = 3x -10

300

Find the general form of the equation of the line that passes through (2, -3) and is perpendicular to 2x+5y=4.

5y + 2x + 11 = 0

400

Find the general form of the equation of the line that passes through (-2, 5) parallel to the line 

2x - 3y -12 = 0

2x - 3y + 19 = 0

500

Find the equations in standard form of the lines that pass through (8, 2) and are

a. parallel to the line 3x - 2y = 9

b. perpendicular to the line 4y + 5x -12 = 0

parallel: y =(3/2)x - 10

perpendicular: y = (4/5)x -22/5

Inverses

100

Find the equation of the inverse.

y = 3x + 2

y = (x-2)/3

200

Find the equation of the inverse.

y = (1/2)x +8

y = 2x - 16

300

Find the equation of the inverse.

y = √(x+5)

y = x²-5

400

Find the equation of the inverse. 

y = 4^x

y = log₄x

500

Find the equation of the inverse.

y = 1/((2)(4^x))

y = log_(1/4)2x