Algebra II Module 6 Quest 2 Review

Operations on Functions

100

If f(x) = x + 5 and g(x) = x - 4, find (f + g)(x)

2x + 1

200

If f(x) = x + 5 and g(x) = x - 4, find (f - g)(x)

9

300

If f(x)= x + 5 and g(x) = x - 4, find (f * g)(x)

x² + x - 20

400

If g(x) = -3x and h(x) = 4x - 1, find g[h(x)] AND h[g(x)].

g[h(x)]= -12x + 3

h[g(x)] = -12x - 1

500

If f(x) = 3x, g(x) = x + 4 and h(x) = x² - 1, 

find h[f(-3)]

80

Inverse Functions and Relations

100

What is the inverse of the relation?

A = {(3, 1), (4, -3), (8, -3), (9, 0)}

A^'= {(1, 3), (-3, 4), (-3, 8), (0, 9)}

200

Find the equation of the inverse of f(x) = 3x

f^-1(x)= x/3

300

Find the inverse of f(x) = 2x - 1 and graph both equations.

f^-1(x) = (x - 1)/2 or

f^-1(x) = (1/2)x - 1/2

400

Find the inverse of the function and graph both.

f(x) = (1/4)x

f^-1(x) = 4x

500

Find the inverse of the function and then graph both.

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

f^-1= 6x - 18

Square Root Functions

100

Is the graph of a square root function that is positive called a "swoosh" or a "scoop?"

swoosh

200

Describe the following graph: y = (sqrt of x) + 3 

swoosh

up 3

300

Describe the following: y = -(sqrt x - 3)

scoop

right 3

400

Graph the following and give the domain and range in interval notation.

y = -(sqrt x + 2) - 1

scoop 

left 2

down 1

D: [-2, infinity)  R: (-infinity, -1]

500

Graph the following and give the D and R in interval notation.

y = 2(sqrt x - 5) + 3

swoosh, steeper

right 5

up 3

D: [5, infinity) R: [3, infinity)

Rational Exponents

100

Write 11^1/7 in radical form.

7th root of 11

200

Write the cubed root of 3a⁵b² in exponential form.

3^1/3a^5/3b^2/3

300

Simplify 216^1/3 using base numbers.

6

400

Simplify (x^1/6)^4/3

x^2/9

500

Simplify the 8th root of (49a¹⁶b⁸)

a²b times the 4th root of 7

Solving Radical Equations

100

solve:  (the square root of x) -1 = 4

x = 25

200

Solve: (square root of x - 5) = 4

x = 21

300

solve: v^1/2 + 1 = 4

v = 9

400

Solve: 10 - (square root of 2x) = 5

x = 12.5

500

Solve: 2 times [the square root of (3x + 4)] + 1 = 15

x = 15