Final Review

Transformations

100

How would you show UP 5 in function notation

f(x) + 5

200

How would you show LEFT 3 in function notation

f(x+3)

300

What transformations are occurring here: f(x - 2) - 4

Right 2

Down 4

400

What transformations are occurring here:

-f(x + 2) - 5

flip over x-axis

left 2

down 5

500

Where is the lowest point in the graph |x + 3| + 1

(-3, 1)

Function Notation

100

If f(x) = x² + 3x - 5, what is f(-2)

-7

200

What type of function is x³

Cubic

300

If f(x) = 3x - 5, find: f(½)

-1

400

What is the y-intercept of (x + 3)(x-1) + 6

3

500

What is the domain and range of:

√(x - 2)

D: [2, inf)

R: [0, inf)

Factoring

100

Factor: 3x³ - 6x² + 9x

3x(x² - 2x + 3)

200

Factor the quadratic: x² + 5x + 6

(x + 2)(x + 3)

300

Factor: 2x² + 5x + 2

(2x + 1)(x + 2)

400

25x² - 16

(5x + 4)(5x - 4)

500

Factor by splitting the middle term:

x³ + 3x² - 4x - 12

(x² - 4)(x + 3)

Vertex Form

100

What value would make a perfect square trinomial:

x² + 12x + ___

36

200

Convert to Vertex Form:

x² - 14x + 50

(x - 7)² + 1

300

Use the quadratic formula to find x-intercepts:

x² + 4x - 7

{-4 ⁺_- √(44)}/2

400

Convert to Vertex Form:

2x² + 16x + 11

2(x + 4)² - 21

500

What is the domain and range of the function:

y = x² + 3x + 6

D: (-inf, inf)

R: [3.75, inf)

Complex Numbers

100

Simplify:√(-64)

8i

200

Simplify: (3i + 2) + (2i - 5)

5i - 3

300

Simplify: (3 - 2i)(5 + 4i)

23+2i

400

Simplify i³⁴

-1

500

Simplify: ^{3i - 1}⁄_2i

^{i + 3}⁄₂