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7.1 Transformations of Graphs
7.1 Transformations of Graphs
Algebra Refresher
Complete the table.
-
| [latex]t[/latex] |
[latex]0[/latex] |
[latex]\dfrac{\pi}{2}[/latex] |
[latex]\pi[/latex] |
[latex]\dfrac{3\pi}{2}[/latex] |
[latex]2\pi[/latex] |
| [latex]t+\dfrac{\pi}{6}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
-
| [latex]t[/latex] |
[latex]0[/latex] |
[latex]\dfrac{\pi}{2}[/latex] |
[latex]\pi[/latex] |
[latex]\dfrac{3\pi}{2}[/latex] |
[latex]2\pi[/latex] |
| [latex]t-\dfrac{\pi}{6}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
-
| [latex]x[/latex] |
[latex]0[/latex] |
[latex]\dfrac{\pi}{2}[/latex] |
[latex]\pi[/latex] |
[latex]\dfrac{3\pi}{2}[/latex] |
[latex]2\pi[/latex] |
| [latex]x-\dfrac{\pi}{3}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
-
| [latex]x[/latex] |
[latex]0[/latex] |
[latex]\dfrac{\pi}{2}[/latex] |
[latex]\pi[/latex] |
[latex]\dfrac{3\pi}{2}[/latex] |
[latex]2\pi[/latex] |
| [latex]x+\dfrac{\pi}{3}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\hphantom{0000}[/latex] |
[latex]\underline{\qquad\qquad\qquad\qquad}[/latex]
Algebra Refresher Answers
-
| [latex]t[/latex] |
[latex]0[/latex] |
[latex]\dfrac{\pi}{2}[/latex] |
[latex]\pi[/latex] |
[latex]\dfrac{3\pi}{2}[/latex] |
[latex]2\pi[/latex] |
| [latex]t+\dfrac{\pi}{6}[/latex] |
[latex]\dfrac{\pi}{6}[/latex] |
[latex]\dfrac{2\pi}{3}[/latex] |
[latex]\dfrac{7\pi}{6}[/latex] |
[latex]\dfrac{5\pi}{3}[/latex] |
[latex]\dfrac{13\pi}{6}[/latex] |
-
| [latex]t[/latex] |
[latex]0[/latex] |
[latex]\dfrac{\pi}{2}[/latex] |
[latex]\pi[/latex] |
[latex]\dfrac{3\pi}{2}[/latex] |
[latex]2\pi[/latex] |
| [latex]t-\dfrac{\pi}{6}[/latex] |
[latex]\dfrac{-\pi}{6}[/latex] |
[latex]\dfrac{\pi}{3}[/latex] |
[latex]\dfrac{5\pi}{6}[/latex] |
[latex]\dfrac{4\pi}{3}[/latex] |
[latex]\dfrac{11\pi}{6}[/latex] |
-
| [latex]x[/latex] |
[latex]0[/latex] |
[latex]\dfrac{\pi}{2}[/latex] |
[latex]\pi[/latex] |
[latex]\dfrac{3\pi}{2}[/latex] |
[latex]2\pi[/latex] |
| [latex]x-\dfrac{\pi}{3}[/latex] |
[latex]\dfrac{-\pi}{3}[/latex] |
[latex]\dfrac{\pi}{6}[/latex] |
[latex]\dfrac{2\pi}{3}[/latex] |
[latex]\dfrac{7\pi}{6}[/latex] |
[latex]\dfrac{5\pi}{3}[/latex] |
-
| [latex]x[/latex] |
[latex]0[/latex] |
[latex]\dfrac{\pi}{2}[/latex] |
[latex]\pi[/latex] |
[latex]\dfrac{3\pi}{2}[/latex] |
[latex]2\pi[/latex] |
| [latex]x+\dfrac{\pi}{3}[/latex] |
[latex]\dfrac{\pi}{3}[/latex] |
[latex]\dfrac{5\pi}{6}[/latex] |
[latex]\dfrac{4\pi}{3}[/latex] |
[latex]\dfrac{11\pi}{6}[/latex] |
[latex]\dfrac{7\pi}{3}[/latex] |
- Identify the amplitude, period, and midline o