Algebra 2 interim review

Foundations

100

Determine the domain of the function

f(x) = 2x²-3x+3

(-infty,+infty)

200

Determine the range of:

y= -x²+5

(-infty,5]

y≤5

300

Let y=x².  Write the function that transforms y by reflecting it across the x-axis, vertical stretch of 4, shifted left 3 units and down 2 units.

y= -4(x+3)²-2

400

Determine the inverse of the function

y=-4x+10

y=-(1/4)x+(5/2)

500

Solve for x

2(2x-5)-2x+4 = -18

x = -6

Absolute Value

100

Solve |2x+1|=9

x=4, and x=-5

200

Solve and state extraneous solutions (if any)

|x-4|=2

x=2, x=6

300

Solve the inequality and write in interval notation

|3x-6|≤9

-3≤x≤5

400

Solve

|x-4|>2(x+1)

x=(2/3)

500

Find all real solutions

|x²-4x-5|=5

x=4, x=0

Radical Functions

100

Simplify √(50)

5√2

200

Solve √(x+3)=5

x=22

300

State the domain of √(4-x)

(-infty,4]

or

x≤4

400

Solve and check for extraneous solutions

√(2x+1)=x-1

x=4

500

Solve -5 = (x+7)^1/2-11

x=29

Systems

100

Solve the system

x+y=10

x-y=2

(6,4)

200

Classify the system as one solution, two solution, no solution, or infinitely many solutions

2x+4y=9

x+2y=4

No solutions

300

Solve the nonlinear system

y=x²

y=2x+3

x=3, x= -1

400

Solve the 3 by 3 system:

x-3y+3z = -4

2x+3y-z = 15

4x-3y-z = 19

(x,y,z)=(5,1,-2)

500

Determine the number missing to make this system have an integer solution. (no decimals)

3x-5y=7

_x+2y=10

2

Polynomial Functions

100

Factor completely

x² - 9

(x+3)(x-3)

200

Complete the operation:

(4x²+5x+7)+(3x²-8x+12)

7x²-3x+19

300

Complete the operation

(3x³-5x+8)-(7x²+6x-9)

3x³-7x²-11x+17

400

Change from vertex form to standard form:

3(x-2)²+10

3x²-12x+22

500

How many zeros are there for the function

x⁴-4x³+4x²

4 zeros

x=0 (multiplicity 2)

x=2 (multiplicity 2)