PreCalculus Jeopardy!

Functions and Relations

100

Determine whether the relation is a function:

{(1,2),(2,3),(3,4),(1,5)}

Not a function (input 1 has two outputs: 2 and 5)

200

Find the domain and range of:

{(−1,3),(0,0),(2,5),(4,5)}

• Domain = {−1, 0, 2, 4}

• Range = {0, 3, 5}

300

 Function value

If f(x)=2x+3, find f(4)

f(4)=2(4)+3=11

400

Evaluate a function

Given g(x)=x²−1, find g(−3)

g(−3)=(−3)²−1=9−1=8

500

Does the graph of a circle represent a function? Explain.

No, because it fails the vertical line test (one x-value has multiple y-values)

Polynomial and Rational Functions

100

Find the zeros of

f(x)=x²−9

x=-3, 3

200

Factor completely

x²+5x+6

(x+2)(x+3)

300

What is the end behavior of:

f(x)=−2x³+x

• As x→∞, f(x)→−∞
• As x→−∞, x→∞

400

Simplify

(x²−9)\(x - 3)

x+3, where x≠3

500

Find the horizontal asymptote of

f(x)=(2x+1)/(x−3)

y=2
(same degree → ratio of leading coefficients)

Exponential and Logarithm Functions

100

Solve exponential equation

2^x=16

x=4

200

Solve using logarithms

3^x=20

x≈2.73

300

A population grows as

P=200(1.1)^t

Find the population after 3 years.

266.2

400

Convert to exponential form

log⁡₂(8)=x

2^x=8

500

Evaluate logarithm

log⁡₁₀(1000)

3

Matrices and Determinant

100

Simplify 

200

Identify element a₂₃ from A = 

What is a₂₃ = 2

300

What term do we use to describe a matrix that places a column of constants in the same matrix as the coefficients.

Augmented Matrix

400

What is the formula for the determinant of a 2x2 matrix?
[ a b ]
[ c d ]

What is ad - bc?

500

Evaluate the determinant of
[ 6 -2 ]
[ 5  1 ]

What is 16?

Conic Section

100

Find the center and radius x^2 + (y + 8)^2 = 9

what is center being (0,-8)

radius 3

200

Find the vertices: 

y²/16 - x²/36=1

(0,4) and (0,-4)

300

Where is the center of the ellipse?

(x-2)²/9 + (y-1)²/4=1

(2,1)

400

Is the graph a parabola, circle, ellipse, or hyperbola?

x² + 25y²=50 

Ellipse

500

Locate the foci of the equation:

x²/4 - y²/1 =1

(±sqrt(5),0)