MathJeopardy!

Reverse! Inverse!

100

For the one-to-one function f(x)=2x+3, find the equation of the inverse.

f^-1(x)=x/2-3/2

200

For the one-to-one function f(x)=x/3-3, find the equation of the inverse.

f^-1(x)=3x+9

300

If a function f(x) is one-to-one, then an inverse function of f(x) exists. TRUE/FALSE?

TRUE!

400

Using the graph of f(x)=x²+2, for x>=0, define two ordered pairs of f^-1(x). I will graph f(x) on the front board for you!

(2,0), (6, 2), (11, 3)

500

Is the function f(x)=-(x²)for x>= 0 one-to-one? Give one or two points that demonstrate this.

The y-coordinate is the same and the x-coordinate is different. ie. (1,-1) and (-1,-1). 

Look at This Photo[graph]...

100

Suppose f(x)=-5|x|. Give one of the two transformations from the parent graph g(x)=|x| to the graph of f(x).

1. Flipped over the x-axis.

2. Stretched vertically by a factor of 5.

200

Suppose f(x)=(x+3)²+4. Give two of the two transformations from the parent graph g(x)=x² to the graph of f(x).

1. Horizontal shift: 3 units to the left.

2. Vertical shift: 4 units up.

300

Graph the line  f(x)=1/2 * x and label 2 points. Hold it up so I may check on it!

Answers may vary, but the line goes through the origin and has a slope of 1/2. Two example points: (0,0), (2,1)

400

Graph the function f(x)=-2^x. Label 2 points on the graph of f(x)

Answers may vary, but as x tends to neg. infinity, f(x) tends to 0 and as x tends to infinity, f(x) tends to infinity. Example points: (0,-1), (1, -2)

500

Graph the perpendicular line to the line y=3x-1, which goes through the point (0,6).

Answer must be a line of slope -1/3 and y-intercept (0,6).

No Bums on this Log[arithm]!

100

Expand the logarithmic function log₂ 2x³. 

log₂2+3log₂x=1+3log₂x

200

Write (or say) the single logarithm function of log₂(x+2)-1/2log₂y.

log₂(x+2)/y^1/2

300

Solve log₃x=-2.

1/9

400

Solve log₃9=x-1.

x=3

500

Suppose 200=100e^0.12t. Solve for t. Round to the third decimal place.

t=(ln 2)/0.12, which is approximately 5.776.

Girl, you're so [de]fiiiine...

100

This is the highest or lowest point of a parabola.

VERTEX

200

This is a logarithm with a base of 10.

COMMON LOGARITHM

300

The  ________________ expression y=log_b x is equivalent to the expression x=b^y.

LOGARITHMIC

400

Two linear equations that have infinitely many solutions in common is said to be _________________ equations.

DEPENDENT

500

A function is said to be __________________  if every element from the range comes from exactly one element in the domain.

ONE-TO-ONE

Missy Lannyous

100

Let f(x)=-(x²)+1 and g(x)=2x-2. Find f(1)-g(-2).

 f(1)-g(-2)=6

200

The larger of two numbers is 4 more than twice the smaller. If the smaller is subtracted from the larger, the result is 7. Write the system of two variables (x and y) which will find the two unknown numbers.

y=2x+4 and y-x=7

300

Let the system be y-1/2 * x=2 and 2y-x=3. Find the solution set.

Empty set. The terms cancel and the resulting statement is false.

400

Find the vertex of f(x)=x²-2x+1

(1, 0)

500

Find the x-intercept and y-intercept of of f(x)=1/2x+1

x-int: (-2,0)

y-int: (0,1)