1 / 28

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

Given g(x) = 2x 2 +1 , find g(3). g(3)=2(3) 2 +1. g(3)=2(9)+1. g(3)=19. Given f(x) = 3x - 1, find 4[f(4) – f(2)]. Given h(x) = 5+5x, find [f(4) – f(1)](-2). 3.3 Linear Functions The student will be able to:. 1. identify linear functions. 2. write equations in standard form.

gregorycarter
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Given g(x) = 2x2 +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 FunctionsThe 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 FormAx + By = CA, 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. • 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. Determine whether each equation is a linear equation. 2) 2x2 - 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

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

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

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

  12. Is this equation linear?y = -3 • Yes • 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: y-intercept: • Set y=0 • Set x=0 • Solve for x • Solve for y 0=10x-1 y=10(0)-1 +1 +1 1=10x y=-1 x=1/10

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

  21. Draw “the river” • Subtract 2x from both sides - 2x - 2x y = -2x + 4 1) Review: Solve for y2x + y = 4 2) Solve for y: 4x + 2y = -6 - 4x - 4x 2y = -4x - 6 2 2 y = -2x - 3 • Subtract 4x • Simplify • Divide both sides by 2 • Simplify

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

  23. Review: Make a t-tableIf 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) x f(x) ordered pair -2 -1 0 1 2

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

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

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

  27. Which is the graph of y = x – 4? • . • . • . • .

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

More Related