1) Draw the graph of the following relation and state the domain and range f(x)=\left\{\begin{array}{ll}

4, & x>1 \\

5, & x=1 \\

x+3, & -2

5-x^{2} & x \leq-2

\end{array}\right.

Domain: ______________________

Range: ______________________ Determine:10 \text { a) } \lim _{x \rightarrow-2^{-}} f(x)= \text { b) } \lim _{x \rightarrow-2^{+}} f(x)= \text { c) } \lim _{x \rightarrow-2} f(x)= d\rparen \lim_{x\rightarrow1^-}f(x)=_{} \text { e) } \lim _{x \rightarrow 1^{+}} f(x)= \text { f) } \lim _{x \rightarrow 1} f(x)= \text { g) } \quad f(1)=

2) Sketch the graph of the function that satisfies the following conditions.

\text { b) Evaluate one-sided limits to determine if } \lim _{x \rightarrow 1} f(x) \text { exists. } \text { c) Determine and verify if the function is continuous at } x=1 \text {. }

4) The height, h, in metres, of a football after it is kicked is represented by h(t)=-4.9 t^{2}+5.2 t+0.75, \text { where } t \text { is time in seconds. } a) Determine the average rate of change of the height of the football in the first second.Interpret your answer. b) Using the difference quotient, determine the instantaneous rate of change of the height of the football at 2 seconds. Interpret your answer. APPLICATION: (16 marks)

5) Evaluate the limit, if it exists. 6) Using First Principles, determine the equation of the line that is perpendicular to the tangent of the curve_ y = √x² − 3 at the point where x = 2. 7) Evaluate the limit, if it exists. 8) Find constants a and b such that the function is continuous.