Algebra I S2 Final Review!

Piecewise Functions

100

What is the domain and range of the function f(x)=|x|?

Domain: all real numbers
Range: y is greater than or equal to 0

200

What is the difference between a ceiling function and a floor function?

Ceiling function: you round up to the nearest integer

Floor function: you round down to the nearest integer

300

Evaluate: f(x)=ceiling(x); x=11.2

12

400

Identify the vertex and axis of symmetry:

p(x)=|x|+3

vertex: (0,3)

AOS: x=0

500

How can you reflect the graph of f(x)=3|x+2| across the x-axis?

Make 3 a negative number.

Exponential Functions

100

What is 3^-3?

1/27

200

What is the solution?
16^x+2=4^3x

x=4

300

The most basic form of an exponential function is f(x)=a*b^x. What does a represent?

y-intercept; initial amount; starting amount

400

What is the difference between an arithmetic and a geometric sequence?

Arithmetic sequence: numbers are being added or subtracted; has a common difference

Geometric sequence: numbers are being multiplied; has a common ratio

500

Write an exponential function for the set of points in the form of f(x)=a*b^x

(0,3),(1,12),(2,48),(3,192)

f(x)=3*4^x

Polynomials and Factoring

100

Simplify. Write the answer in standard form.
(3x²+4x+2)-(-x+4)

3x²+5x-2

200

Name the polynomial based on its degree and number of terms: 7x³+xy+4

cubic trinomial

300

Find the product:

(2x-5)(3x²+4x-1)

6x³-7x²-22x+5

400

Rewrite in factored form:

x²-11x+10

(x-10)(x-1)

500

Factor and tell me, what is this special case called?
9x²-100

(3x+10)(3x-10); difference of two squares!

Quadratic Functions

100

What is the vertex and axis of symmetry for the graph f(x)=x²?

vertex: (0,0)
AOS: x=0

200

How does the value of a affect the graph when compared to the graph of the quadratic parent function?
g(x)=-5x²

more narrow and reflection over x-axis

300

What is the vertex and axis of symmetry for the function h(x)=(x+1)²?

Vertex: (-1,0)
AOS: x=-1

400

What is the y-intercept of f(x)= -0.3x²-0.6x-0.2?

(0,-0.2)

500

What is the vertex of the function: f(x)=x²+2x+4?

vertex: (-1,3)

More Math! (Random)

100

Write an exponential growth or decay function for the following situation: Initial value of 200 increasing at a rate of 5%

y=200(1.05)^x

200

Write the function of a graph after a shift 1 unit right and 4 units up: f(x)=|x|+2

New function: |x-1|+6

300

What is the common ratio of the geometric sequence?
30, 6, 1.2, 0.24, 0.048...

common ratio is 0.2 or 1/5

400

Find the GCF of the pair of monomials: 12a⁵b and 16a⁴b²

GCF= 4a⁴b

500

Consider the function f(x)=ax². What happens to the range when a is negative?

Range: y is less than or equal than 0