1. Given g(x) = 2x 2 +1, find g(3) g(3)=2(3) 2 +1 g(3)=2(9)+1 g(3)=19

2. Given f(x) = 3x - 1, find 4[f(4) – f(2)]

3. Given h(x) = 5+5x, find [f(4) – f(1)](-2)

4. 3.3 Linear Functions The student will be able to: 1. identify linear functions. 2. write equations in standard form. 3. Graph linear functions. Indicators: Designed by Skip Tyler, Varina High School

5. Vocabularies A linear equation is the equation of a line. An x-intercept is a point on the graph where y is zero. In other words, an x-intercept is a point in the equation where the y-value is zero. A y-intercept is a point on the graph where x is zero. In other words, a y-intercept is a point in the equation where the x-value is zero. Values of x for which f(x)=0 are called zeros. For a linear function, the zero is its x-intercept.

6. Standard Form Ax + By = C A, B, and C have to be integers An equation is LINEAR (the graph is a straight line) if it can be written in standard form. This form is useful for graphing (later on…).

7. Determine whether each equation is a linear equation. 1)4x = 7 + 2y Can you write this in the form Ax + By = C? 4x - 2y = 7 A = 4, B = -2, C = 7 This is linear!

8. 2) 2x 2 - y = 7 Can you write it in standard form? NO - it has an exponent! Not linear 3) x = 12 x + 0y = 12 A = 1, B = 0, C = 12 Linear Determine whether each equation is a linear equation.

9. Here’s the cheat sheet! An equation that is linear does NOT contain the following: 1.Variables in the denominator 2.Variables with exponents 3.Variables multiplied with other variables. xy = 12

10. Is this equation linear? 1.Yes 2.No Standard Form x – 4y = 3

11. Is this equation linear? 1.Yes 2.No Exponents are not allowed!

12. Is this equation linear? y = -3 1.Yes 2.No Standard Form 0x + y = -3

13. Review of the definition. An x-intercept is a point on the graph where y is zero. In other words, an x-intercept is a point in the equation where the y-value is zero. A y-intercept is a point on the graph where x is zero. In other words, a y-intercept is a point in the equation where the x-value is zero. Values of x for which f(x)=0 are called zeros. For a linear function, the zero is its x-intercept.

14. Determine the x-intercept, y-intercept, and zero of the linear equation y=10x-1. x-intercept: Set y=0 Solve for x 0=10x-1 +1 +1 1=10x x=1/10 y-intercept: Set x=0 Solve for y y=10(0)-1 y=-1

15. Determine the x-intercept, y-intercept, and zero of the linear equation y=10x-1. x-intercept:y-intercept:

16. Find the x-intercept, y-intercept, and zero for the graph of the line. Solution: The x-intercept of this graph is 4. The coordinates of the point at the x-intercept is (4, 0). The y-intercept of this graph is 2. The coordinates of the point at the y-intercept is (0, 2).

17. Find the x-intercept, y-intercept, and zero for the graph of the line. x-intercept: -3 y-intercept: 3 zero: 3

18. Work on the following problems: P 158 #3, 12-19 all,

19. Graph an equation by making a table

20. Graphing Steps 1)Isolate the variable (solve for y). 2)Make a t-table. If the domain is not given, pick your own values. 3)Plot the points on a graph. 4)Connect the points.

21. 1) Review: Solve for y 2x + y = 4 1.Draw “the river” 2.Subtract 2x from both sides - 2x - 2x y = -2x + 4 2) Solve for y: 4x + 2y = -6 1.Subtract 4x 2.Simplify 3.Divide both sides by 2 4.Simplify - 4x - 4x 2y = -4x - 6 2 2 y = -2x - 3

22. 3) Solve for y: x - 3y = 6 1.Subtract x 2.Simplify 3.Divide both sides by -3 4.Simplify - x - x -3y = -x + 6 -3 -3 or

23. 4)Review: Make a t-table If f(x) = 2x + 4, complete a table using the domain {-2, -1, 0, 1, 2}. 2(-2) + 4 = 0(-2, 0) 2(-1) + 4 = 2(-1, 2) 2(0) + 4 = 4(0, 4) 2(1) + 4 = 6(1, 6) 2(2) + 4 = 8(2, 8) xf(x) -2 0 1 2 ordered pair

24. 5)Given the domain {-2, -1, 0, 1, 2}, graph 3x + y = 6 -3(-2) + 6 = 12(-2, 12) -3(-1) + 6 = 9 (-1, 9) -3(0) + 6 = 6 (0, 6) -3(1) + 6 = 3 (1, 3) -3(2) + 6 = 0 (2, 0) x-3x + 6 ordered pair 1.Solve for y: 3x + y = 6 Subtract 3x - 3x - 3x y = -3x + 6 2. Make a table -2 0 1 2

25. Bonus questions! What is the x-intercept? (2, 0) What is the y-intercept? (0, 6) Does the line increase or decrease? Decrease 5)Given the domain {-2, -1, 0, 1, 2}, graph 3x + y = 6 3.Plot the points (-2,12), (-1,9), (0,6), (1,3), (2,0) 4.Connect the points.

26. 5)Given the domain {-2, -1, 0, 1, 2}, graph 4x + 2y = 6

27. 1.. 2.. 3.. 4.. Which is the graph of y = x – 4?

28. P 158 36-37, 39-43 odds ( might change due to time consuming)