Precalculus S1W2 Flipped Classroom

1

what are the end conditions to even polynomial functions with a negative leading coefficient?

positive side goes up, negative side goes down

positive side goes down, negative side goes up

both sides go up

both sides go down

both sides get close to 0 without ever touching

1

List some ways to categorize or analyze functions

1

Watch the following video link about limits https://precalculus.flippedmath.com/23-limits-graphically.html
Do you have any questions, or want anything in particular clarified?

1

You may have used limits last year to express end conditions. What is the following limit
It may be easier to be able to read this aloud as "the limit as x approaches infinity of negative three x to the fifth minus 7"

0

does not exist

1

Same exact question as the q1, but with limits in the answers. what are the end conditions to even polynomial functions with a negative leading coefficient?

limit as x approaches infinity and negative infinity is asymptotically close to 0, from above on the positive side from below on the negative side

limit as x approaches infinity is infinity, limit as x approaches negative infinity is negative infinity

limit as x approaches infinity is negative infinity, limit as x approaches negative infinity is positive infinity

limit as x approaches infinity and negative infinity is both the same, and both positive infinity

limit as x approaches infinity and negative infinity is both the same, and both negative infinity

1

continuous and discontinuous are another way to analyse and categorize functions. Think through the graph for y=1/x (put it in desmos, if you would like.) which category would you place this graph.

continuous

jump discontinuous

infinitely discontinous

1

notation exercise: in the following limit notation, what does the + mean in 0+?

It is only asking for positive answers for 1/(x-4) as x gets close to 4

it is only asking for the trend when you put positive numbers into the equation

it is only specifying that the 4 is positive

it is only asking for the trend on the right side of the line x=4

1

A limit does not exist if the limit of the function coming from one direction doesn't equal the limit coming from the other direction. Can you think of a scenario where the limit from one side doesn't exist either?

1

what is the limit of the following graph as x approaches 0?

0

does not exist

1

We still have some review to cover. Watch this video on transformations
https://precalculus.flippedmath.com/41-transformations.html
Do you have any questions or have concepts you would like clarified?

1

How does f(x)+2 transform f(x) differently than f(x+2)

f(x)+2 shifts horizontally, while f(x+2) shifts vertically

f(x)+2 shifts vertically, while f(x+2) shifts horizontally

f(x)+2 stretches horizontally, while f(x+2) compresses vertically

f(x)+2 compresses vertically, while f(x+2) stretches horizontally

1

How does 2f(x) transform f(x) differently than f(2x)

2f(x) shifts horizontally, while f(2x) shifts vertically

2f(x)shifts vertically, while f(2x) shifts horizontally

2f(x) compresses horizontally, while f(2x) stretches vertically

2f(x)stretched vertically, while f(2x) compresses horizontally

1

For 2f(x) +3 would you stretch first and then shift, or would you shift first and then stretch? explain why.

1

Mathematically speaking, what are the criteria for a function to be continuous? Honors, you should be able to answer this without the hint.

1

Remember piecewise functions? they are like frankenstein functions: pieces of different functions stitched together across your domain. Which color part of the graph would you follow to find the limit of y as x approaches -1+

red

blue

green

purple

1

Sort the topics from this week into where you understand them

What is a limit
how can you tell if a limit exists
when it is clear that a limit does not exist
what is the purpose of a limit
what are discontinuities
what is the difference between a jump discontinuity, a removable discontinuity and an infinite discontinutity
what is the difference between continuous and smooth
what do you do to a function to make it shift up or down
what do you do to stretch or compress a function horizontally or vertically
how do you read or right limits
What does it mean to take a one-sided limit

I've got this
I'm fuzzy
so confused

Precalculus S1W2 Flipped Classroom

what are the end conditions to even polynomial functions with a negative leading coefficient?

List some ways to categorize or analyze functions

Watch the following video link about limits https://precalculus.flippedmath.com/23-limits-graphically.htmlDo you have any questions, or want anything in particular clarified?

You may have used limits last year to express end conditions. What is the following limitIt may be easier to be able to read this aloud as "the limit as x approaches infinity of negative three x to the fifth minus 7"

Same exact question as the q1, but with limits in the answers. what are the end conditions to even polynomial functions with a negative leading coefficient?

continuous and discontinuous are another way to analyse and categorize functions. Think through the graph for y=1/x (put it in desmos, if you would like.) which category would you place this graph.

notation exercise: in the following limit notation, what does the + mean in 0+?

A limit does not exist if the limit of the function coming from one direction doesn't equal the limit coming from the other direction. Can you think of a scenario where the limit from one side doesn't exist either?

what is the limit of the following graph as x approaches 0?

We still have some review to cover. Watch this video on transformationshttps://precalculus.flippedmath.com/41-transformations.htmlDo you have any questions or have concepts you would like clarified?

How does f(x)+2 transform f(x) differently than f(x+2)

How does 2f(x) transform f(x) differently than f(2x)

For 2f(x) +3 would you stretch first and then shift, or would you shift first and then stretch? explain why.

Mathematically speaking, what are the criteria for a function to be continuous? Honors, you should be able to answer this without the hint.

Remember piecewise functions? they are like frankenstein functions: pieces of different functions stitched together across your domain. Which color part of the graph would you follow to find the limit of y as x approaches -1+

Sort the topics from this week into where you understand them

what are the end conditions to even polynomial functions with a negative leading coefficient?

List some ways to categorize or analyze functions

Watch the following video link about limits https://precalculus.flippedmath.com/23-limits-graphically.htmlDo you have any questions, or want anything in particular clarified?

You may have used limits last year to express end conditions. What is the following limitIt may be easier to be able to read this aloud as "the limit as x approaches infinity of negative three x to the fifth minus 7"

Same exact question as the q1, but with limits in the answers. what are the end conditions to even polynomial functions with a negative leading coefficient?

continuous and discontinuous are another way to analyse and categorize functions. Think through the graph for y=1/x (put it in desmos, if you would like.) which category would you place this graph.

notation exercise: in the following limit notation, what does the + mean in 0+?

A limit does not exist if the limit of the function coming from one direction doesn't equal the limit coming from the other direction. Can you think of a scenario where the limit from one side doesn't exist either?

what is the limit of the following graph as x approaches 0?

We still have some review to cover. Watch this video on transformationshttps://precalculus.flippedmath.com/41-transformations.htmlDo you have any questions or have concepts you would like clarified?

How does f(x)+2 transform f(x) differently than f(x+2)

How does 2f(x) transform f(x) differently than f(2x)

For 2f(x) +3 would you stretch first and then shift, or would you shift first and then stretch? explain why.

Mathematically speaking, what are the criteria for a function to be continuous? Honors, you should be able to answer this without the hint.

Remember piecewise functions? they are like frankenstein functions: pieces of different functions stitched together across your domain. Which color part of the graph would you follow to find the limit of y as x approaches -1+

Piecewise functions are written with brackets like so: if you were looking to find the limit as x approaches -1+ would you be looking at

Where in the graph are there jump discontinuities?

Where is there an infinite discontinuity?

Honors: Give an example of a function with a removable discontinuity.

Sort the topics from this week into where you understand them

Piecewise functions are written with brackets like so: if you were looking to find the limit as x approaches -1+ would you be looking at

Where in the graph are there jump discontinuities?

Where is there an infinite discontinuity?

Honors: Give an example of a function with a removable discontinuity.

Watch the following video link about limits https://precalculus.flippedmath.com/23-limits-graphically.html
Do you have any questions, or want anything in particular clarified?

You may have used limits last year to express end conditions. What is the following limit
It may be easier to be able to read this aloud as "the limit as x approaches infinity of negative three x to the fifth minus 7"

We still have some review to cover. Watch this video on transformations
https://precalculus.flippedmath.com/41-transformations.html
Do you have any questions or have concepts you would like clarified?

Watch the following video link about limits https://precalculus.flippedmath.com/23-limits-graphically.html
Do you have any questions, or want anything in particular clarified?

You may have used limits last year to express end conditions. What is the following limit
It may be easier to be able to read this aloud as "the limit as x approaches infinity of negative three x to the fifth minus 7"

We still have some review to cover. Watch this video on transformations
https://precalculus.flippedmath.com/41-transformations.html
Do you have any questions or have concepts you would like clarified?

Piecewise functions are written with brackets like so:
if you were looking to find the limit as x approaches -1+ would you be looking at

Piecewise functions are written with brackets like so:
if you were looking to find the limit as x approaches -1+ would you be looking at