1 / 13

Section 3.4 Basic Functions

Constant Function. Section 3.4 Basic Functions. Linear Function Identity. Square Function Quadratic. Section 3.4 Basic Functions. Cubic Function. Cube Root Function. Section 3.4 Basic Functions. Absolute Value Function. Rational Function. Section 3.4 Basic Functions. Square Root

petec
Download Presentation

Section 3.4 Basic Functions

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. Constant Function Section 3.4 Basic Functions Linear Function Identity

  2. Square Function Quadratic Section 3.4 Basic Functions Cubic Function

  3. Cube Root Function Section 3.4 Basic Functions Absolute Value Function

  4. Rational Function Section 3.4 Basic Functions Square Root Function

  5. Greatest Integer Function Section 3.4 Basic Functions

  6. Continuous Functions Is a function where the graph has no gaps, holes, or breaks…it can be drawn without stopping and lifting your pencil. Section 3.4 Basic Functions Discontinuous Functions Is a function where the graph has gaps, holes, or breaks…it can not be drawn without stopping and lifting your pencil.

  7. Piecewise-Function { for for for Find the following… Find the inequality that is true for the value of x and plug the value into the function. 2. What is the domain of the function? Use the individual domain restrictions to find the entire domain.

  8. Piecewise-Function { for for for 3. Find all intercepts. Y-intercept is when x = 0 or f(0). The y-intercept is at ( 0, -1 ). x-intercepts are when y = f(x) = 0. Take each individual function and set it equal to zero. Not true. The x-intercept is at ( 1, 0 ). x = 1 is ok, but -1 violates domain. Not possible, ½ is not in the domain.

  9. Piecewise-Function { for for for 4. Graph the function. Test all endpoints given in the domain restrictions. Color coordinate the functions. Test the -3 and -1 for the first function. -2(-3) + 1 and -2(-1) + 1 6 + 1 = 7 2 + 1 = 3 ( -3, 7 ) ( -1, 3 ) Open point because of no equal to line. Closed point because of equal to line. Test the -1 for the third function, but it will be an open point. This is a quadratic function, so we will test points, 0, 1, 2, etc. Test the -1 for the second function. This is a constant function with only x = -1, yields the point ( -1, 2 ). (-1)2 – 1 = 0 ( -1, 0 ) (1)2 – 1 = 0 ( 1, 0 ) (3)2 – 1 = 8 ( 3, 8 ) (0)2 – 1 = -1 ( 0, -1 ) (2)2 – 1 = 3 ( 2, 3 )

  10. Piecewise-Function { for for for 5. Use the graph to determine the range. Use your pencil as a horizontal line. Start at the lowest point on the graph and slide your pencil up. Identify all the y – coordinates that your touching. No 6. Is f continuous on its domain?

  11. Piecewise-Function { 4. Graph the function.

  12. Piecewise-Function { 1. What is f(-2), f(5), and f(-1 )? 2. What is the domain of the function?

  13. Piecewise-Function { 3. Find all intercepts. x intercepts y intercept 5. Find the Range. 6. Is f continuous on its domain? No

More Related