# Problem 1

Draw the graphs of the following equations in two variables *x *and *y*.

- −3
*x*+ 2*y*= 2 *x*= 1- (
*x*+ 2)^{2 }= 2(2*y*+ 1) - (
*x*+ 2)^{2 }+ (*y*− 3)^{2 }= 6 - For each of the examples above, determine whether it is the graph of a function
*y*=*f*(*x*). If so, find*f*(*x*), its domain, and its range. - For each of the examples above, determine whether it is the graph of a function
*x*=*g*(*y*). If so, find*g*(*y*), its domain, and its range.

# Problem 2

Let *f*(*x*) = 2^{x/}^{2}. Find the inverse function of *f*, denoted *f*^{−1}, and state domain and range of *f *and *f*^{−1}.

Note that *f*^{−1 }is common symbolic notation for the inverse function. It does, however, **not **denote the function 1*/f*(*x*)!

# Problem 3

Compute following limits

- a) lim
_{x}_{→1}*x*^{2 }+ 2*x*− 2

b)

c)

d)

e)

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