Advanced Functions Jeopardy

Remainder Theorem

100

Find the remainder when f(x)+x²+2 ÷ (x-1)

R=3

200

Find the remainder when: f(x)=14x²-22x-4 ÷ (4x+8)

R=96

300

When f(x)=3x³+9x²-15x-3 ÷ (3x-2), determine R.

R= -73/9

400

Determine the value of k when x²+kx ÷ (x-2) and R=24.

k=10

500

Determine the value of k when 4x³+12x²+kx-6 ÷ (2x-1)

k=19

Y-Intercepts

100

What is a y-intercept?

A y-intercept is where the line of a graph crosses the y-axis.

200

Among these values, what is the y-intercept? (Picture 1)

(0,2)

300

Solve for the y-intercept. y=-1/2(x+4)²+3

y=-5

400

Find the y-intercept for the following. y=6log(x+3)+1

y=3.86

500

Find the y-intercept(s) for the piece-wise function. (Picture 2)

y=2

y=8

Writing Equations Using Transformations

100

What is the general equation for a logarithmic function?

y= alog(k(x+d))+c

200

List the transformations for the following function: y= 2log(x+4)+5

Vertical stretch by 2, horizontal translation left 4 units, vertical translation up 5 units.

300

Using this function, what would the new points be? y=2(x+4)²+5

(-6,13), (-5,7), (-4,5), (-3,7), (-2,13)

400

A new bridge is being built close to the old one for slower moving trucks. Using the bridge as a base (f(x)=-x²), the new bridge will be horizontally stretched by 6 units. Due to its different location, horizontally translated 8 units left of the old bridge and 3 units down. What does this equation look like?

f(x)= -(1/6(x+8))-3

500

Which function is written correctly based on the graphs? a)y=-2(x+2)²-4  b) y=3(x+9)²+3 

c) y=-2(x-4)²-4  d) y=5(x+2)²+7 (Picture 3)

A

Horizontal Asymptotes

100

What is the horizontal asymptote for the graph? (Picture 4)

+1

200

Find the horizontal asymptote for x/2x-1 .

1/2

300

Does this graph have a horizontal asymptote? If so, what is it? (Picture 5)

There is no horizontal asymptote, only a slant asymptote.

400

Find the horizontal asymptote for: 3-2x²/ 3x²+3x+1

-2/3

500

Find the horizontal asymptote for: (4x+3) (2x+1) / (x²-4) (2x+5)

0

Writing Families

100

What does a family of polynomials all possess?

They have the same zeros/ x-intercept.

200

Determine the equation of a family with zeros at 6 and -13.

y= a (x-6) (x+13)

300

Which set of polynomials belong to the same family? a) -2(x+3)(x-4), 5(x+4)(x-3) b) 7(x-8)(x+9), 13(x+9)(x-8)

B

400

Which family of polynomials does this equation belong to? 4x²+10x+6 

a) a(2x+3)(x+1)  b) a(4x+2)(4x+3)  c) a(x+3)(x+2)  d) a(2x+1)(x+3)

A

500

Determine the equation of a function with zeros at 1 +/- √3 and -1/3 and simplify.

y= a (x³- 5/3x²- 8/3x- 2/3)