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