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1.Share how you remember transformations. Do you have any tips or hints that help you to remember?
I had to answer this blog along time of go. The reason I did not answer it, was because I forgot how to do transformations. But know I found out how to do it. My friends form the Calculus class helped me remember how to do it. They told me that if I add or subtract a number to x, my graph would shift to the right or to the left.
For example
When you graph -ln(x+3) you have to move 3 units to the left. (At the begging of the class, I believed that I had to move 3 units to right because I was add 3 to x but I was wrong.)
The reason I remember that the graph should go either left or right is because my friends told me that I have to moves OPPOSITE way when you are add or subtract sign.
3. What still confuses you or worries you about trigonometry?
What still worries me is finding the zeros of the graph. My domain and range a little bit.
1. What is the DIFFERENCE between finding the limit of a function at x=c and actually plugging in the number x=c? When are the two cases the SAME?
When you are try to find the limit at x=c you are also find the output and the value of f(x) when it gets closer to c. There could be holes at x=c, but for the limit to exist the hole has to be removable. This is calling a Removable Discontinuity.
The two cases are the same when the graph of the function is continuous.
* When the angle, θ is 0°
cos=1, sin=0 and tan=0
* when θ is 90°
cos=0, sin=1 and tan is undefined
This is how the unit circle.
The another thing, I learned was the domain and range. The frist things I thing you should know is that most points, being a relationship between certain x's and certain y's, is a relation. The domain is all the x-values, and the range is all the y-values.
Domain: {2, 3, 4, 6}
Range: {–3, –1, 3, 6}
I also learned the one-to-one function. A one to one function is a function in which every element in the range of the function corresponds with one and only one element in the domain.
Example of a one-to-one function:
{ (0,1) , (5,2), (6,4) }
Domain: 0, 5, 6
Range: 1,2, 4
Each element in the domain (0, 5, and 6) correspond with a unique element in the range. Therefore this function is a one-to-one function
DEFINITION OF EVEN AND ODD FUNCTIONS
Even functions
If you let f(x) be a real-valued function of a real variable. Then you will get a equation that has the follow: f(−x) = f(x) (for all the real number of x ).
Even function graphs are always symmetrical with the y-axis.
Examples of even functions are x^2, x^4, x^6, cos(x) [even function includes only even powers]
Example use the cos (x):
f(-x) = -cos7(-x)
-cos (-7x)
-cos7x
f(-x) = f(x)
Example of graphs for Even Functions:
Odd Functions Again, let f(x) be a valued function of a real variable. Then if f is odd you will get the following equation: f(-x) = -f(x) (for all real numbers of x).
The odd function's graph is always be symmetric to the origin. Examples of odd functions are x, x^3, x^9, sin(x) [odd function includes only odd powers]
Example use sin (x):
f(-x) = sin (-3x)
-sin(3x)
f(-x) = -f (x)
Examples of graphs for Odd Functions: