Algebra II Review

Simplifying Exponential Expressions

100

(x⁴y²)(x³y)

x⁷y³

200

5^-3

1/125

300

(3x⁶y²)³

27x¹⁸y⁶

400

(x^5/4)(x^2/3)

Write your answer in radical form.

The 12^th root of x²³.

500

(x^1/3y^1/5)¹⁵

x⁵y³

Function Operations and Composition

100

Let f(x)=5x-2 and g(x)=3x+8.

Find (f+g)(10).

(f+g)(10)=86

200

Let f(x)=5x-2 and g(x)=3x+8.

Find (g-f)(2).

(g-f)(2)=6

300

Let f(x)=5x-2 and g(x)=3x+8.

Find (fg)(x).

(fg)(x)=15x²+46x-16

400

Let f(x)=5x-2 and g(x)=3x+8.

Find f(g(3)).

f(g(3))=83

500

Let f(x)=5x-2 and g(x)=3x+8.

Find g(f(x)).

g(f(x))=15x+2

Polynomials

100

Simplify completely:

(2x²+3x-8)+(3x²-5x+3)

5x²-2x-5

200

Simplify completely:

(8x-2)-(3x+5)

5x-7

300

A triangle has side lengths of (3x-2), (5x+10), and (-2x²+1). What is the perimeter of the triangle?

-2x²+8x+9

400

The length of a rectangle is 5x-4 and the width is 3x. What is the area of the rectangle?

15x²-12x

500

The length of a ribbon is 18x³+9x²-6x. The ribbon is being cut into 3 pieces of equal length. What is the length of one of the pieces?

6x³+3x²-2x

Graphs

100

What is the difference between a maximum and minimum? Describe in words or draw and label a picture.

Maximums are the points where graphs change from increasing to decreasing. Minimums are the points where graphs change from decreasing to increasing.

200

Sketch a graph of the polynomial with roots at -4, -2, 1, and 5.

Graph shaped like a W with points on the x-axis at -4, -2, 1, and 5.

300

Write the equation of a polynomial with roots of -6, -1, and 3 that approaches negative infinity on the right.

f(x)=-(x+6)(x+1)(x-3)

400

Sketch a graph of the polynomial:

y=(x-5)(x+1)(x+3)

N shaped graph with x-intercepts at (5,0), (-1,0), and (-3,0).

500

Sketch the graph:

f(x)=-x(x-4)(x+2)(x+7)

Upside down W with roots at 0, 4, -2, and -7.

Inverse Relations

100

What is the inverse of (-3,2), (0,2), and (5,-1)?

(2,-3)

(2,0)

(-1,5)

200

What would be the slope of the graph that is the inverse of y=2/3x+5?

3/2

300

Find the inverse of y=2x-5

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

400

Find the inverse of f(x)=x³+5

The inverse of the function is the third root of x-5.

500

The inverse represents a reflection over what line?

An inverse is a reflection over the line y=x.