Math 141 Exam 1 Review

Rational Functions

100

True or False in a rational function there is always a slant asymptote? 

False 

200

Find the horizontal asymptotes of y=(x² -9)/(x³-x)

y=0

300

Find the slant asymptote

x²+3x+2 

_______

x-1

x+4

400

find the HA, VA and holes in the equation. 

2x²-12x+16

__________

x²-x-12

y=2

x=-3

holes x=4

500

Determine what intervals the function is positive.  

3x² -5x+2

_________

x²-4

(-infinity,-2) and (2, infinity) 

Inverse functions

100

Do all functions have a inverse? when does a function not have a inverse?

no ; when it fails the horizontal line test 

200

solve the inverse y=2x+6

f^-1= (x-6)/2

300

Determine Whether the function is ONE-TO-ONE.

a) 𝒉 = {(𝟒, −𝟓), (𝟔, 𝟏), (𝟐, 𝟒), (𝟎, −𝟑)

yes 

400

find the inverse 

5x+2

_____

9x-5

f⁻¹(x) = (5x + 2) / (9x - 5).

500

A local water park charges an entrance fee of $5 per person, plus an additional $2 per hour for the use of its waterslides. The total cost, C(x), for one person using the waterslides for x hours can be modeled by the function: C(x)=2x+5 where  C(x) is the total cost in dollars, and x is the number of hours spent on the waterslides.  If a person has a certain amount of money, say y dollars, how many hours can they spend on the waterslides? Find the inverse of the function C(x)=2x+5 and use it to determine how many hours a person can spend on the waterslides if they have $23.

9 hours 

Exponential functions

100

what is the parent function of a exponential function?

f(x)=AB^x

200

from the function how can you tell if a function is growth or decay?  

Growth: B>1

Decay: B<1

300

is this equation growth or decay 

y=-6(-5^6x)

Growth 

400

How will this equation shift my graph? y=e^x+5+4

Up 4; left 5 

500

The half life of rubidium 445 is 1,890 years the amount present A after T years is represented by 

A=½^(t/1,890)

How much sample is there after 100 years (NO CALCULATOR!!)

A= ½^(100/1890)

Graphs and Applications

100

What is the Vertical line test do?

determines if a graph is a function? 

200

sketch y= 2x/x²-4

show 

400

would you rather have a Penney that doubles every day for 30 days or 1 million dollars? 

what kind of function is this?

penny that doubles would result in $5,368,709.12

Exponential 

 

500

Susan wants to have $7,500 in her savings account after 36 months. The bank offers an annual interest rate of 6.5%, compounded continuously. How much money should Susan invest now to reach her goal of $7,500 in 36 months?

A=Pe^rt

P=

7500

_________

e0.065×3

SI Sessions

100

What is my Major?

Civil Engineering 

200

Who is the other Math 141 SI Leader 

Camila 

300

How many images or gifs of the Muppets did I use in my slides?

3

400

How many gifs (not images) did I use in my slides? 

10

500

What 4 games have I played during my SI sessions

Jeopardy, kahoot, battleship, and Jenga