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### Section 3.5 : Graphing Functions

For problems 1 – 13 construct a table of at least 4 ordered pairs of points on the graph of the function and use the ordered pairs from the table to sketch the graph of the function.

1. $$f\left( x \right) = 6x - 1$$
2. $$f\left( x \right) = 3 - 5x$$
3. $$f\left( x \right) = 2{x^2}$$
4. $$f\left( x \right) = {x^2} + 7$$
5. $$f\left( x \right) = \sqrt {x + 3}$$
6. $$f\left( x \right) = \sqrt {6 - x}$$
7. $$\displaystyle f\left( x \right) = \frac{1}{x}$$ , use only positive $$x$$’s
8. $$\displaystyle f\left( x \right) = \frac{1}{x}$$ , use only negative $$x$$’s
9. $$f\left( x \right) = \left\{ {\begin{array}{*{20}{l}}3&{{\rm{if }}x \ge 0}\\{4 - x}&{{\rm{if }}x < 0}\end{array}} \right.$$
10. $$f\left( x \right) = \left\{ {\begin{array}{*{20}{l}}{4x}&{{\rm{if }}x \le - 2}\\{3 - 2x}&{{\rm{if }}x > - 2}\end{array}} \right.$$
11. $$f\left( x \right) = \left\{ {\begin{array}{*{20}{l}}{2 - {x^2}}&{{\rm{if }}x < 1}\\{{{\left( {x - 2} \right)}^2}}&{{\rm{if }}x \ge 1}\end{array}} \right.$$
12. $$f\left( x \right) = \left\{ {\begin{array}{*{20}{l}}{{x^2}}&{{\rm{if }}x > 3}\\4&{{\rm{if }} - 2 \le x \le 3}\\{1 - x}&{{\rm{if }}x < - 2}\end{array}} \right.$$
13. $$f\left( x \right) = \left\{ {\begin{array}{*{20}{l}}{1 - x}&{{\rm{if }}x \ge 1}\\{{x^2} - 1}&{{\rm{if }} - 1 < x < 1}\\{ - 1 - x}&{{\rm{if }}x \le - 1}\end{array}} \right.$$