Alg 2 Chapter 5 Jeopardy

Writing Inverse Equations

100

If g(x) = -4x + 1, find g^-1(x).

g^-1(x) = - ^x/₄ + ¹/₄  or 

g^-1(x) = ^-(x-1)/₄

200

If h(x) = ¹/_x - 2, find h^-1(x).

h^-1(x) = ¹/_(x+2)

300

If f(x) = 2x³ + 3, find f^-1(x).

f^-1(x) = cube root of [^(x-3)/₂]

400

If t(x) = (x+5)^1/2, find t^-1(x).

t^-1(x) = x² - 5 where x is greater than or equal to 0

500

If b(x) = (3x² - 6)/2, find b^-1(x).

b^-1(x) = plus or minus the square root of (^2x/₃ + 2)   OR   plus or minus the square root of [^{(2x + 6)}/₃]

Inverse Graphs & Tables

100

Find the inverse table for the following points: 

(3,7) (-2,6) (-11,-2)

(7,3) (6,-2) (-2,-11)

200

Find the inverse table for the following points:

(-3,3) (-2,2) (-1,1) (0,0) (1,1) (2,2) (3,3) 

(3,-3) (2,-2) (1,-1) (0,0) (1,1) (2,2) (3,3)

300

What is the line of symmetry between a graph and its inverse?

y = x

400

What is the shape of a quadratic's inverse and is that inverse a function?

A sideways parabola and it is not a function.

500

Give two different parent functions whose inverse graphs are identical to the original graphs.

Linear (y = x)

Hyperbola (y = ¹/_x)   

Circles (x² + y² = 1)

Converting Log & Exponential Form

100

Rewrite in exponential form: log₃ (9) = 2

3² = 9

200

Convert to log form: 

6^-2 = ¹/₃₆

log₆ (¹/₃₆) = -2

300

Write in exponential form: log_x (64) = 3

x³ = 64

400

Convert to log form: 5^x = 110

log₅ (110) = x

500

Convert to log form: m^z = t

log_m (t) = z

Evaluating Logs

100

Evaluate log₄ (16)

2

200

Find the value of x: 

log_x (125) = 3

x = 5

300

Find x:  log (x) = 4

x = 10,000

400

Find x: log₂ (x) = -3

x = ¹/₈

500

Evaluate log₇ (¹/₃₄₃) 

-3

Function Composition

100

g(x) = x² - 3x + 10 and 

f(x) = -2x + 1.  Find g(-3). 

g(-3) = 28

200

g(x) = x² - 3x + 10 and 

f(x) = -2x + 1.  Find g(f(0)).

g(f(0)) = 8

300

g(x) = x² - 3x + 10 and f(x) = -2x + 1.  

Find f(f^-1(10)).

f(f^-1(10)) = 10 

400

g(x) = x² - 3x + 10 and f(x) = -2x + 1.  

Find f(a+7).

f(a+7) = -2a - 13

500

g(x) = x² - 3x + 10 and f(x) = -2x + 1.  

Find g(g(x)).

g(g(x)) = x⁴ - 6x³ + 26x² - 51x + 80