Schlogl Algebra II - Chapter 7 Test Review Game!

Rational Exponents/Properties

100

convert to radical form. x^2/3

CRTx²

200

7^1/4 * 7^1/2 

7^3/4  *Common base - add exponents

300

(64y⁶ )^1/3

4y²

Function Operations & Composition

100

Given f(x) = 5x, g(x) = x + 2, State the domain of (f/g)(x).

Domain: All Reals where x cannot be -2

(-inf, -2) U (-2, inf)

200

f(x) = 3x -8 and g(x) = 2x². Find the following. g(f(5))

g(f(5)) = 98 

bc. f(5) = 3(5) - 8 = 7 g(7) = 2(7)^2 = 2(49) = 98

300

f(x) = 4x^-1 and g(x) = 5x - 2 Find f(f(x))

x

Inverse Functions

100

Looking at the tables. Are the following inverses? 

A: (0,6) (1,2) (2,3) (-2,8) (5,0)

B: (6, 0) (2,1)(3,2) (8, -2) (0,5)

Yes!

200

Use the VLT and HLT on the graph of f(x) =x². Is f(x) a function? Is f^-1 (x) a function?

f(x) is a function bc f(x) passes the VLT f^-1 (x) is not a function bc f(x) does not pass HLT

300

Find an equation for the inverse of the relation y =3x - 5

y = 1/3 x + 5/3   or  y = (x+5)/3

400

Find the inverse of f(x) = -10x⁶

f^-1(x) = - ( x/-10)^1/6 

Graph Square Root/Cube Root

100

 Domain of y = (x) ^1/2

[ 0, infinity)

200

State the domain & range. y = SQRT (x-2)

Domain: [2, infinity): Range [0, infinity)

300

State the Domain & Range. y = (x-3)^1/2 + 2

Domain: [3, inf)  Range [2, inf)

400

Graph y = sqrt(x-6)

see picture

Solve Radical Equations

100

Given (4x+9)^1/2=5    Is x=4 a solution?

Yes. (4(4)+9)^(1/2)=5 (25)^(1/2)=5 5=5!

200

Given x + 1 = (7x+15)^1/2. Are both, one, or neither of the following solutions? x = 7 or x = -2

The only solution is x=7. x =-2 is extraneous. 

300

Solve (2x + 7)^1/3 = 3.

x = 10  

400

Solve. x+1 = (7x + 15)^1/2 

x = 7  

500

Simplify ((x+2)^1/2 +1)²

x + 3 + 2(x+2)^1/2