Answer:
Check below
Step-by-step explanation:
1. Definition for intervals
![(a,b)=\left \{ x\in\Re : a](https://tex.z-dn.net/?f=%28a%2Cb%29%3D%5Cleft%20%5C%7B%20x%5Cin%5CRe%20%3A%20a%3Cx%20%5C%3Aand%20%5C%3Ax%3Cb%20%5Cright%20%5C%7D%5C%5C%28a%2Cb%5D%3D%5Cleft%20%5C%7B%20x%5Cin%5CRe%20%3A%20a%3Cx%20%5C%3Aand%20%5C%3Ax%5Cleq%20b%20%5Cright%20%5C%7D)
2. Functions
1) ![\Re \rightarrow \Re \\ f(x)=x](https://tex.z-dn.net/?f=%5CRe%20%5Crightarrow%20%5CRe%20%5C%5C%20f%28x%29%3Dx)
Let's perform graph tests.
That's an one to one, injective function. Look how any horizontal line touches that only once. Also, It's a surjective and a bijective one.
2)![\Re\geq0\rightarrow\Re , f(x)=x+1\\](https://tex.z-dn.net/?f=%5CRe%5Cgeq0%5Crightarrow%5CRe%20%2C%20f%28x%29%3Dx%2B1%5C%5C)
Injective, surjective and bijective.
Injective: a horizontal line crosses the graph in one point.
3)![f:\Re\geq 0\rightarrow\Re, f(x) = cos(x)](https://tex.z-dn.net/?f=f%3A%5CRe%5Cgeq%200%5Crightarrow%5CRe%2C%20f%28x%29%20%3D%20cos%28x%29)
The cosine function is not injective, bijective nor surjective.
4)![f:\Re\rightarrow\Re \:f(x)=ex](https://tex.z-dn.net/?f=f%3A%5CRe%5Crightarrow%5CRe%20%5C%3Af%28x%29%3Dex)
Since e, is euler number it's a constant. It's also injective, surjective and bijective.
5) Quite unclear format
![6) \:f:\Re\rightarrow(0,\infty), f(x) =ex](https://tex.z-dn.net/?f=6%29%20%5C%3Af%3A%5CRe%5Crightarrow%280%2C%5Cinfty%29%2C%20f%28x%29%20%3Dex)
Despite the Restriction for the CoDomain, the function remains injective, surjective and therefore bijective.
![7) f:\Re\geq 0 \rightarrow \Re\geq0, f(x) =x^{4}](https://tex.z-dn.net/?f=7%29%20f%3A%5CRe%5Cgeq%200%20%5Crightarrow%20%20%5CRe%5Cgeq0%2C%20f%28x%29%20%3Dx%5E%7B4%7D)
Not injective nor surjective therefore not bijective too.
![8).f:\{-1,2,-3\}}\rightarrow \{1,4,9\}, f(x) =x^{2}](https://tex.z-dn.net/?f=8%29.f%3A%5C%7B-1%2C2%2C-3%5C%7D%7D%5Crightarrow%20%5C%7B1%2C4%2C9%5C%7D%2C%20f%28x%29%20%3Dx%5E%7B2%7D)
![f(-1)=1, f(2)=4, f(-3)=9](https://tex.z-dn.net/?f=f%28-1%29%3D1%2C%20f%282%29%3D4%2C%20f%28-3%29%3D9)
Injective (one to one), Surjective, and Bijective.
![10) f:\Re\geq 0\rightarrow [-1,1], f(x)= cos(x)\\-1=cos(x) \therefore x=\pi,3\pi,5\pi,etc.](https://tex.z-dn.net/?f=10%29%20f%3A%5CRe%5Cgeq%200%5Crightarrow%20%5B-1%2C1%5D%2C%20f%28x%29%3D%20cos%28x%29%5C%5C-1%3Dcos%28x%29%20%5Ctherefore%20x%3D%5Cpi%2C3%5Cpi%2C5%5Cpi%2Cetc.)
Surjective.
![11.f:R\geq 0[-1,1], f(x) = 0\\](https://tex.z-dn.net/?f=11.f%3AR%5Cgeq%200%5B-1%2C1%5D%2C%20f%28x%29%20%3D%200%5C%5C)
Surjective
12.f: US Citizens→Z, f(x) = the SSN of x.
General function
13.f: US Zip Codes→US States, f(x) = The state that x belongs to.
Surjective