1. Translations and Combinations Algebra 5/Trigonometry

2. Shifting What does it mean to shift? (interactive)interactive Vertical Shift c Units Up: h(x) = f(x) + c Vertical Shift c Units Down: h(x) = f(x) – c Vertical Shift c Units Right: h(x) = f(x - c) Vertical Shift c Units Left: h(x) = f(x + c)

3. Try These

4. Reflecting What does it mean to reflect? (interactive)interactive Reflection in the x-axis: h(x) = -f(x) Reflection in the y-axis: h(x) = f(-x)

5. Try These

6. Stretching

7. Try These

8. Arithmetic Combinations of Functions Sum: (f + g)(x) = f(x) + g(x) Difference: (f - g)(x) = f(x) - g(x) Product: (fg)(x) = f(x) ∙ g(x) Quotient: ( )(x) =

9. Compute f(x) = 4x + 2 and g(x) = 2x – 1 f(x) + g(x) f(x) - g(x) fg(x) ( )(x)

10. Now Try These f(x) = x 2 - 9 and g(x) = 3x – 1 f(x) + g(x) f(x) - g(x) fg(x) ( )(x)

11. Composition of Two Functions The composition of the function f with the function g is given by (f o g)(x) = f(g(x)) The domain of (f o g) is the set of all x in the domain of g such that g(x) is in the domain of f.

12. Compositions Given: f(x) = x 2 - 9 and g(x) = 3m, find f(g(x)). find g(f(x)).

13. Now Try These Given f(x) = 6x + 2 and g(x) = 2x – 1 find f(g(x)). find g(f(x)).