BQ#7

Q. Explain in detail where the formula for the difference quotient comes. 

The difference quotient formula comes from a formula that we know very well since the beginning of our high school career. The formula y2-y1/x2-x1. With this formula is where it all started.on a curved graph we use variables to distinguish the unknown points . With the midpoint formula we bring.together the variables

BQ #6 Unit U

1. What is a continuity?
A continuity is a graph that we can draw without lifting our pencil off the paper. It has  no holes jumps or breaks. The value and limit are the same.

Examples:

B) What is a discontinuity?
 There are two discontinuity families:removable and non removable discontinuities.A removable discontinuity is a point discontinuity which is known as a hole.Then we have a jump discontinuity in which the graph looks like it jumps lower i.n the coordinate plane. An oscillating graph looks wiggly because the graph is going up and down so many times we can see it. Finally we have an infinite graph that that results in unbounded behavior near a vertical asymptote.

Examples :

Jump discontinuity

                      Infinite discontinuity

Oscillating discontinuity

2) What is a limit?
A limit is the intended height of the graph. In other words its the height the graph wants to reach but doesn't actually reach it.

B) When does a limit exist?
A limit exists  when the function intends to reach its certain intended height. A limit usually exists with a point discontinuity.

C) When does a limit not exist?
There are 3 situations that a limit doesn't exist; jump,oscillating and infinite discontinuity.
A limit doesn't exist for a jump discontinuity because it "jumps" on the plane. The term its different from the left and right tells us it doesn't have a limit. Then an oscillating graph doesn't have a limit because it has oscillating behavior meaning we can see how many times the graph goes up and down. Finally, an infinite discontinuity doesn't have a limit because of unbounded behavior. The graph goes in opposite directions for infinity.Thos happens when we have a.vertical asymptote.

BQ # 2 Unit R

How do the trig graphs relate to unit
Circle?

A. Why Is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi.

For a sine graph we know that sine is.postive.in the first to.quadrants and negative in quadtants 3and 4. Cosine is positive then negative, its a pattern that goes on forever. 2pi is how long it takes for each pattern to repeat itself. We are unwrapping the unit circle into a straight line.




A tangent and cotangent

BQ #3

How do the graphs of sine and cosine relate to each of the others?

Tangent

In a tangent graph,we relate to the identity of tan equals sin /cos. Cos equals zero and this will tells us where it will lie on the graph.

BQ 5

Why do sin and.cosine nit have asymptotes, but the other four trig graphs do?

Asymptotes are undefined. Sjne and cosine dont have demoninators that equal zero. Sine has the ratio y/r and cosine has a ratio of x/r. In the unit circle r equals 1. Therefore we will always get a value. The other four trig graphs have a possibility of getting value a of zero.

BQ #4 unit R

Why is the period for sine and cosine 2 pi,whereas the period for tangent and cotangent is pi?


The trig graph is a unit circle that is unwrapped. For sine ans cosine, 2pi is how long it takes for the graph to repeat itself.



For tangent and cotangent pi is how long it takes to repeat itself

reflection#1 unit Q Verifying trg identities.

To verify a trig function means to prove the left side if it is correct while not touching the right side. We must prove it is correct because we use our identities to prove them right.

2.I had to memorize the identities because this is what will help us throughout the unit. Another tip.is to.look for identities that we can replace with and have the same . Like sin for the whole equation

3.I start by looking at the left side . I dont touch the right side. We look if we can substitute a identity or reciprocal. We get a a common denominator or gcf. We do all we need to get our answer on the left. This includes several key factors that will help us achieve our proven equation.