1. Target: We will be able to identify parent functions of graphs

2. PARENT FUNCTIONS See handout Constant Function Inverse Linear (Identity)Inverse Squared Absolute Value Exponential Quadratic Logarithmic CubicSquare Root Greatest Integer

3. Constant Function f(x) = a where a = any # Even: Symmetric with y-axis

4. Constant Function Domain: Range: Parent Equation: f(x) = 2 Even: Symmetric with y-axis

5. Constant Function Parent Equation: f(x) = 2 x – intercept: y – intercept: None Even: Symmetric with y-axis

6. Constant Function Graph Description: Horizontal Line Table: xy -22 2 02 12 22 Parent Equation: f(x) = 2

7. Linear Function (Identity) f(x) = x Odd: Symmetric with origin

8. Linear Function (Identity) Domain: Range: Parent Equation: f(x) = x Odd: Symmetric with origin

9. Linear Function (Identity) Parent Equation: f(x) = x x – intercept: y – intercept:

10. Linear Function (Identity) Parent Equation: f(x) = x Table: xy -2 00 11 22 Graph Description: Diagonal Line Odd: Symmetric with origin

11. Absolute Value Function f(x) = │ x │ Even: Symmetric with y-axis

12. Absolute Value Function Domain: Range: Parent Equation: f(x) = │ x │

13. Absolute Value Function Parent Equation: f(x) = │x │ x – intercept: y – intercept:

14. Absolute Value Function Table: xy -22 1 00 11 22 Parent Equation: Graph Description: “V” - shaped f(x) = │ x │

15. f(x) = x 2 Quadratic Function Even: Symmetric with y-axis

16. f(x) = x 2 Quadratic Function Domain: Range: Parent Equation:

17. Quadratic Function Parent Equation: x – intercept: y – intercept: f(x) = x 2

18. Quadratic Function Table: xy -24 1 00 11 24 Parent Equation: Graph Description: “U” - shaped

19. Cubic Function f(x) = x 3 Odd: Symmetric with origin

20. Cubic Function f(x) = x 3 Domain: Range: Parent Equation: Odd: Symmetric with origin

21. Cubic Function f(x) = x 3 Parent Equation: x – intercept: y – intercept:

22. Cubic Function f(x) = x 3 Parent Equation: Table: xy -2-8 00 11 28

23. f(x) = x Square Root Function Neither even nor odd

24. f(x) = x Square Root Function Domain: Range: Parent Equation: Neither even nor odd

25. f(x) = x Square Root Function Parent Equation: x – intercept: y – intercept:

26. f(x) = x Square Root Function Parent Equation: Table: xy 00 11 42 93 164 Graph Description: Horizontal ½ of a Parabola

27. f(x) = 1 x Inverse Function or Rational Function (Reciprocal of x) Odd: Symmetric with origin

28. f(x) = 1 x Inverse Function or Rational Function (Reciprocal of x) Parent Equation: Domain: Range:

29. f(x) = 1 x Inverse Function or Rational Function (Reciprocal of x) Parent Equation: x – intercept: y – intercept:

30. Inverse Function or Rational Function (Reciprocal of x) Table: xy -2-0.5 0Error 11 20.5 f(x) = 1 x Parent Equation: Odd: Symmetric with origin

31. Inverse Squared Function (Reciprocal of x 2 ) f(x) = 1 x 2x 2

32. Inverse Squared Function (Reciprocal of x 2 ) f(x) = 1 x 2x 2 Parent Equation: Domain: Range:

33. Inverse Squared Function (Reciprocal of x 2 ) f(x) = 1 x 2x 2 x – intercept: y – intercept: Parent Equation:

34. Inverse Squared Function (Reciprocal of x 2 ) f(x) = 1 x 2x 2 Parent Equation: Table: xy -20.25 1 0Error 11 20.25

35. Exponential Function b = base and x = exponent Neither even nor odd

36. f(x) = 2 x Exponential Function Domain: Range: Parent Equation: Neither even nor odd

37. f(x) = 2 x Exponential Function x – intercept: y – intercept: Parent Equation:

38. f(x) = 2 x Exponential Function Table: xy -20.25 0.5 01 12 24 Parent Equation: Graph Description: Backwards “L” Curves

39. f(x) = log x Logarithmic Function

40. f(x) = log x Logarithmic Function Range: Parent Equation: Domain:

41. f(x) = log x Logarithmic Function x – intercept: y – intercept: Parent Equation: Neither even nor odd

42. Logarithmic Function Table: xy -2Error Error 0 10 20.301 Parent Equation: f(x) = log x

43. Step Function (Greatest Integer) f(x) = [x] Neither even nor odd

44. Step Function (Greatest Integer) f(x) = [x] Domain: Range: Parent Equation:

45. Step Function (Greatest Integer) f(x) = [x] Parent Equation: x – intercept: y – intercept:

46. Step Function (Greatest Integer) f(x) = [x] Parent Equation: Graph Description: Stair Steps Table: xy -2 00 11 22

47. HW 1.5: Use a graphing calculator, or online graphing utility to graph #19-41 odd, p 71