Shared Flashcard Set

Details

Precalc-Module 1&Module 3
Module 1- Functions
11
Mathematics
Undergraduate 1
11/12/2012

Additional Mathematics Flashcards

 


 

Cards

Term
How do you know when something is a function?
Definition

-Vertical line test-The line can't go through more than one point

-No x values can be repeated

Term
What is the equation for the difference quotient?
Definition
f(x+h)-f(x)/h
Term
What happens when you have a function inside a square root and you have to find its domain?
Definition
you have to make a number line and make sure that everything below and above each number works in the domain. also check if the numbers themselves are in the domain as well.
Term
(f/g)(2)
Definition
What would you do with the 2 in order to set up what this equation is supposed to look like?
Term
How do you find the domain of something like x/x+3? How is this strategy similar from the one for finding the domain of just a normal combination of functions like x^2+2x+3?
Definition

-Make sure to include the domain of each part of the fraction: x and x+3.

-Then, make sure that you make the denominator in any function that involves a quotient equal to 0 and the x-value you get will be another restriction on the domain.

Term
How do you find the domain of two functions added or subtracted?
Definition
Just find the numbers that work for BOTH of the functions.
Term

(not an obvious answer)

-How would you set up the difference quotient for f(x)=x^2-x+4?

Definition

(x+h)^2-(x+h)+4-x^2+4-4

 

-Rembember that the signs of the two last numbers (and also first number when it is orig. a negative number) change because the WHOLE function is being subtracted from the one with x+h replacing x.

Term
If a graph was increasing from (-4,0) to (-2,3) and (2,-3) to (4,0) then how would you formally write this?
Definition

(-4,-2)U(2,4)

 

only take the x-values into account when looking at where it increases/decre. (basically on any intervals)

Term
When asked for the min. and max. of a graph how would you write it?
Definition
you would only write the y-values that are the max./ min. b/c you're basically only looking at the points in the y-axis to determine which one is the highest and lowest on graph.
Term

what would the graph of...look like?

 

-y=x 

-y=x^2

-y=x^3

-y=square root of x

-absolute value of x 

-1/x

Definition

-It would just be a straight tilted line going straight through the middle of the graph.

-It would be a parabola

-It would be a parabola but the right side would be like a normal parabola and the other on the left will be turned upside down.

-it would be the left side of a regular parabola tilted horizontally. (there is no other side)

-would be a wide V shape

-look it up 

 

Term
What would the graph of the distance a bike goes a function of time look like? What does this depend on?
Definition

the graph would keep increasing the whole time but the distance would start to at one point start to increase more slowly so it will level off a bit. 

 

UNLESS it says that the car is traveling at a constant speed which would mean that it's jsut a straight line.

 

Supporting users have an ad free experience!