The document discusses four function families: 1) Linear functions which have the form y = ax + b and form a line. 2) Quadratic functions which have the form y = ax^2 + bx + c and form a parabola. 3) Exponential functions which have the form y = ab^x and form a curve known as an exponential slide. 4) Absolute value functions which have the form y = a|x + b| + c and form a V-shape.

1. Function Families

2. 4 families Linear Quadratic Exponential Absolute Value

3. Linear – Line y =a x +b

4. Quadratic – parabola y =a x 2 +b x +c

5. Exponential – Slide y =a ∙ b x

6. Absolute Value – V y =a │ x +b │ +c

7. Model & Equation? Plot the points using Stat Plot Identify the model

8. Model & Equation? Stat>Calc> 4 Linear 5 Quadratic 0 Exponential

9. Model & Equation? Put equation in Y= to check with points No Absolute Value

10. Model & Equation? (-2, ¼) (–1, ½) (0, 1) (1, 2) (2,4) Exponential y = 2 x

11. Model & Equation? (-2, 3) (–1, 3/2) (0, 1) (1, 3/2) (2,3) Quadratic y = ½ x 2 + 1

12. Model & Equation? (-2, -3) (–1, -1) (0, 1) (1, 3) (2, 5) Linear y = 2 x + 1

13. Review What are the names and shapes of the four function families?