PreCalculus Chapter 1 Review

Holes and Asymptotes

100

Find the Hole

x/ (x²-2x)

Hole at x=0

200

Find the Vertical Asymptote:

x/ (x²-2x)

VA at x=2

300

True of False:

Flamingos bend their legs at the Knee

False: They bend their legs at the ankle, not at the knee.

400

Find the Holes and the Vertical Asymptotes:

f(x)= (x²-3x)/(3x²+6x)

Hole at x=0

VA at x=2

500

Find all Restrictions of the Domain and Range for this function:

f(x)= (x+4)/ (x²+x-12)

Hole at x=-4

VA at x=3

HA at y=0

Characteristics of Functions

100

Find the Domain and Range of x²+4

D: All real numbers

R: [4, infinity)

200

Find the Increasing and Decreasing Intervals for the following Function:

3 - (x - 1)²

Increasing: (- infinity, 1]

Decreasing: [1, infinity)

300

Is this function Even, Odd, or Neither?

3/(1+x²)

Even

400

True or False: Ice pops were invented by a child by accident.

True: An 11-year-old boy named Frank Epperson left soda powder and water outside overnight with its wooden stirrer still in the cup. The mixture had frozen in the chilly nighttime weather, and so the Epsicle was born

500

Find the Domain:

x/(x²-5x)

(- infinity, 0) U (0,5) U (5, infinity)

Hole at x=0; VA at x=5

Equations and Word Problems

100

Solve: 10x²-20x-80=0

x=4

x=-2

200

Solve: x²-16x+39=0

x=3

x=13

300

Solve: 8x²+64x+120=0

x=-3

x=-5

400

True or False:

Sloths can hold their breath longer than dolphins can

True: By slowing their heart rates, sloths can hold their breath for up to 40 minutes. Dolphins can only hold their breath for 10 minutes

500

Solve: 11x²+4x+12=0

(-2+8i√2)/11

(-2-8i√2)/11

Inverses

100

Find the Inverse:

f(x)=3x-2

(x+2)/3

200

Find the Inverse:

f(x)=3x-6

y=(x+6)/3

300

True or False:

Froot Loops loops all have different flavors

False: Froot Loops loops are all the same flavor

400

Find the Domain of this function's inverse:

f(x)=(x+3)/(x-2)

( - infinity, 1) U (1, infinity)

500

What's the difference between the Vertical Line test and the Horizontal Line Test?

Vertical line test determines whether or not something is a function. The Horizontal Line Test determines whether something has an inverse.

Miscellaneous

100

Determine whether this function is Even, Odd, or Neither

f(x)=x³-4

Neither

200

Is it impossible to hum while holding your nose?

Yes... You tried it didn't you?

300

An airplane 30,000 feet above the ground begins descending at a rate of 2,000 feet per minute. Write an equation to model the situation. Find the altitude of the plane after 5 minutes.

y=-2000+30,000

20,000 ft

400

How many hearts to Octopi have?

3: One pumps blood to their whole systems, and two are dedicated just to the gills

500

You buy a DVD player for $80 and then some DVDs for $10 each. How many DVDs did you buy if you spent $200? AND What is the y-intercept of this situation?

y=10x+80

b = 80