1. Additional Trig Graphs Apply the same process to tangent and other trig functions (5.6)

2. POD Give the amplitude, period, and shifts for f(x). Give the “anchor” interval.

3. POD Give the amplitude, period, and shifts for f(x). Give the “anchor” interval. Amplitude = 2The “anchor” Period = 8 interval runs from Phase shift = 4/π 4/π to 8 + 4/π.

4. Moving to… … tangent. The process today is the same as what we looked at last time. The main differences are 1. the period of a transformed tangent function is π/|b|. 2. there is no “amplitude” (although we do have a vertical scale change of |a|). 3. the “anchor” interval is –π/2 < bx + c < π/2.

5. Try it Find the period, shifts, and vertical scale change for g(x). How does the point (π/4,1) translate with that vertical scale change? (This will help with homework.)

6. Try it Find the period, shifts, and vertical scale change for g(x). Here, a = ½, and the period remains π. Because a=½, the graph is compressed vertically by half. There is no vertical shift. The phase shift is –π/4. That means the point (0, 0) on the parent shifts to (–π/4, 0). One interval is –3π/4 < x < π/4.

7. Try it Find the period, shifts, and vertical scale change for g(x). The graph is compressed vertically by half. The phase shift is –π/4. The point (π/4,1) becomes (0, ½)

8. Reciprocal functions If we were to transform the reciprocal functions, how would they compare to their parent functions? Look on page 401.

9. Reciprocal functions If we were to transform the reciprocal functions, how would they compare to their parent functions? The cotangent function works the same as tangent, except the anchor interval is based on 0 ≤ bx + c ≤ π.

10. Reciprocal functions If we were to transform the reciprocal functions, how would they compare to their parent functions? Any vertical scale change for secant and cosecant affects the relative extrema– the distance between the inside points– rather than amplitude. The distance between them is 2a.

11. Reciprocal functions If we were to transform the reciprocal functions, how would they compare to their parent functions? The anchor intervals also shift: secant–π/2 ≤ bx + c ≤ 3π/2 cosecant0 ≤ bx + c ≤ 2π (The book shows –π ≤ bx + c ≤ π. Either will work, just keep track of how the curves face.)

12. Try it Try graphing this reciprocal function by hand. You can start by graphing the parent function.

13. Try it Try graphing this reciprocal function by hand. You can start by graphing the parent function. The period is π, and the spread between relative extrema is 4 rather than 2. The anchor interval is 0 ≤ x ≤ π.

14. Try it Here we can compare the parent function. Notice how the relative extrema are spread twice as far apart, and the period is half as wide. The anchor interval is placed from 0 to π.

15. Try it How is the phase shift reflected in this graph? The point (0, 1) moves to (–π/4, 2).

16. And another if there’s time What do you think this looks like?

17. And another if there’s time What do you think this looks like?