Unit K WPP 8

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WPP 7

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Unit K: Student Problem 10

We split up the decimal and know that the first term would be .4. That becomes 4 over 10 (we want to use fractions in this problem). To Find r, we put the second term over the first term, so: .04 over .4 which equals .1.

Next we need to plug into our infinite geometric formula.  The first term is 4/10, so we write that, and multiply by .1 (which is r) raised to n-1. We multiply this out and cross cross the denominator with the reciprocal, we are left with 4/9.

This problem is about using the infinite geometric formula for a sequence with a repeating decimal (we need to rationalize it). You should pay attention to cross canceling and plugging things in to the correct area.

Unit K: Fibonacci Haiku

Unit J Concept 6: Student Problem 6

Details: this concept is similar to concept 5, however we have repeating factors here. so we must remember to correctly count up with exponents in the denominator. other than that, it's the same steps, and remember to substitute back correctly.
Remember to FOIL and combine like terms correctly!

Unit J Concept 5 Student Problem

Details:

This is about partial fraction decomposition (with distinct factors). We learn how to break a fraction apart (helpful for calculus). Several steps include composing, combining like terms, and factoring (and skills from concept 1). We focus on the denominator.

Make sure to pay attention to the steps when you are looking for the common denomintaor and the multiplication that is involved (FOIL correctly!!)

Edmodo is down.

not sure if a 4 on a WSQ needs to be resubmitted, so just playing it safe.

Unit I, Concept 1


The exponential yak died expression means that the asymptote is y=k with no restrictions in the domain.
One way to find if there is not an x-intercept is to set y=0, and if it becomes undefined that means that there is none. Also you can just look at the graph.
To correctly write the range of the graph you use exponential notation, negative infinity to the asymptote.
We can tell when the graph is below when a is negative; the graph will be on top if a is positive.

WPP #6

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unit G pre-test PMI

P: these quizzes helped me to review for the test. Without them i would not have had as much practice.
M: the downside of this was that i found them challenging and I had to study more, which took more time.
I: i'm surprised i passed all my quizzes.

Student Problem 3 Unit I, Concept 1

This is about exponential functions and how to solve/graph them step by step. The reader needs to pay attention to the key points, the y-intercept, x-intercept, and the asymptote!

Unit G Summary Question (Concepts 1-7a thru 1-7b): #10

Unit G Summary Question (Concepts 1-7a thru 1-7b): #10

10. While the domain of a rational function depends on DIVAH, what do you think the range of a rational function depends on? Give an example.
this is because the domain is dependent on the asymptotes or any existing holes, and the domain is related to the range, so that is why there is a relationship between all these concepts.

Unit G Summary Question (Concepts 1-7a thru 1-7b): #9

Unit G Summary Question (Concepts 1-7a thru 1-7b): #9

9. Describe how to find the x-intercept(s) of a rational function. Include both the long way and the shortcut way, explaining why the shortcut makes mathematical sense.

set factors equal to zero, multiply by denominator to cancel. then we solve for x.

Unit G Summary Question (Concepts 1-7a thru 1-7b): #6

Unit G Summary Question (Concepts 1-7a thru 1-7b): #6

6. How do we find the appropriate place to plot a hole if the y-value is undefined when plugged into the original equation?

set it equal to zero then solve!

Unit G Summary Question (Concepts 1-7a thru 1-7b): #8

Unit G Summary Question (Concepts 1-7a thru 1-7b): #8

7. How do you find the y-intercept of a rational function? Does this need to be done in the original or simplified equation?

-we should first plug in a zero for every X variable
-use the original equation!!

Unit G Summary Question (Concepts 1-7a thru 1-7b): #7

Unit G Summary Question (Concepts 1-7a thru 1-7b): #7

7. Describe how to write limit notation for vertical asymptotes and what notation means.

this is similar to the limit notation of end behavior, it is written as, as x--->1- , f(x) ---> -∞  and as x---> 1+ , f(x) ---> ∞

it is simply just stating what is going on in the graph (whether it be going up or down, left or right)

Unit G Summary Question (Concepts 1-7a thru 1-7b): #5

Unit G Summary Question (Concepts 1-7a thru 1-7b): #5

5. Describe the conditions in which a graph can cross through the asymptote.

the graph can cross through horizontal and slant asymptotes, however it never passes through vertical asymptotes

Unit G Summary Question (Concepts 1-7a thru 1-7b): #4

Unit G Summary Question (Concepts 1-7a thru 1-7b): #4

4. What is the difference between a graph having a vertical asymptote and a graph having a hole?

the biggest difference between the two is that vertical asymptote will show where the graph will approach, the hole is where it approaches.

Unit G Summary Question (Concepts 1-7a thru 1-7b): #3

Unit G Summary Question (Concepts 1-7a thru 1-7b): #3

3. When does a graph have a slant asymptote? How do you find the equation for a slant asymptote?

-only when degree is one bigger than the degree of the denominator
-use long division to find the equation of a slant asymptote

 

Unit G Summary Question (Concepts 1-7a thru 1-7b): #2

Unit G Summary Question (Concepts 1-7a thru 1-7b): #2
Limit Notation for horizontal asymptotes

What is basically happening is that the graph is moving left or right towards infinity, but it will not move up and down towards infinity, rather, towards a number (the asymptote).

example:As x---> +∞, f(x)---> #  x---> -∞, f(x)--->#

Unit G Summary Question (Concepts 1-7a thru 1-7b): #1

Unit G Summary Question (Concepts 1-7a thru 1-7b): #1
 How to tell if a graph has a horizontal asymptote. What are the three options?

We must compare the degrees of the numerator and the denominator first!!
1. Bigger degree on bottom, the asymptote is y=0

2. degree is the same, then it is the ration of the coefficients
3. degree is bigger on top, there is no horizontal asymptote.