Ahhh this week has been long it almost slipped my mind to post, but no need to worry I will make this post extra long!

I figured to make up for lost time I might as well go over the worksheet for this week…

#1 a) How many functions are there from (x){1,2,3} to (y){1,2,3,4,5}?

–personally speaking it is easier for me to look at functions vertically (like elementary school), it gives me the ability to draw lines between the two functions.

To find how many functions it is the number of elements in the second function powered to the number of elements in the first function, therefore the answer is 5^3.

b) How many of them are onto?

–this is where drawing the functions vertically really helps

none of them are onto because every element in y is not an output for f

c) How many of them are one-to-one

3 functions are one-to-one because the three elements in x go to a different output

#2 a) How many functions are there from (x){1,2,3,4,5} to (y){1,2,3}?

similar to before y^x thus, 5^3

b) How many of them are onto?

there are 69 functions that are onto…getting 69 takes alot of addition

c) How many of them are one-to-one?

none because the five elements in x can’t go to different outputs in y

#3

a) If f & g are surjective, then g0f is surjective–True the best explanation my group could think of was that g is the co-domain of f therefore if both are surjective their composite with also be surjective

b) If g0f is surjective, then f is surjective–false

f(x)=sqrt (X), g(x)= y^2

#4 (because I have trouble using latex I am just going to write our explanations of each statement)

a) the statement states that the functions are not onto

b) If 3/(n^2), then 3/n (are group couldn’t figure out a simpler way to put it)

c) f is a decreaseing function

#5 Due to my inability to latex and the mere fact that two of the problems are due for ths weeks homework I will pass this question!

Phewwwwwww!!! If you have any questions or comments feel free to respond 🙂

GOOD LUCK ON THE MIDTERM TOO!!!