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Section 1-10 : Common Graphs

Without using a graphing calculator sketch the graph of each of the following.

  1. \(\displaystyle y = \frac{4}{3}x - 2\) Solution
  2. \(f\left( x \right) = \left| {x - 3} \right|\) Solution
  3. \(g\left( x \right) = \sin \left( x \right) + 6\) Solution
  4. \(f\left( x \right) = \ln \left( x \right) - 5\) Solution
  5. \(\displaystyle h\left( x \right) = \cos \left( {x + \frac{\pi }{2}} \right)\) Solution
  6. \(h\left( x \right) = {\left( {x - 3} \right)^2} + 4\) Solution
  7. \(W\left( x \right) = {{\bf{e}}^{x + 2}} - 3\) Solution
  8. \(f\left( y \right) = {\left( {y - 1} \right)^2} + 2\) Solution
  9. \(R\left( x \right) = - \sqrt x \) Solution
  10. \(g\left( x \right) = \sqrt { - x} \) Solution
  11. \(h\left( x \right) = 2{x^2} - 3x + 4\) Solution
  12. \(f\left( y \right) = - 4{y^2} + 8y + 3\) Solution
  13. \({\left( {x + 1} \right)^2} + {\left( {y - 5} \right)^2} = 9\) Solution
  14. \({x^2} - 4x + {y^2} - 6y - 87 = 0\) Solution
  15. \(\displaystyle 25{\left( {x + 2} \right)^2} + \frac{{{y^2}}}{4} = 1\) Solution
  16. \(\displaystyle {x^2} + \frac{{{{\left( {y - 6} \right)}^2}}}{9} = 1\) Solution
  17. \(\displaystyle \frac{{{x^2}}}{{36}} - \frac{{{y^2}}}{{49}} = 1\) Solution
  18. \(\displaystyle {\left( {y + 2} \right)^2} - \frac{{{{\left( {x + 4} \right)}^2}}}{{16}} = 1\) Solution