1 / 14

Do Now 10/09/2015

Learn how to graph and solve equations involving absolute value functions. Understand the V-shape graph, vertex, slope, and symmetry. Practice identifying and graphing absolute value functions.

cachenbach
Download Presentation

Do Now 10/09/2015

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. Do Now 10/09/2015 • Solve given equations.

  2. 2.1 Graphing Absolute Value Functions CC2

  3. Absolute value • written as ⎜x⎟, represents the distance between x and 0 on a number line. As a distance, absolute value is always positive. For every point on a number line, there is another point on the opposite side of 0 that is the same distance from 0. For example, both 5 and –5 are five units away from 0. Thus, ⎜−5⎟ = 5 and ⎜5⎟ = 5.

  4. Absolute Value is defined by:

  5. The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x To the right of x = 0 the line is y = x Notice that the graph is symmetric in the y-axis because every point (x,y) on the graph, the point (-x,y) is also on it.

  6. y = a |x - h| + k • Vertex is @ (h,k) & is symmetrical in the line x=h • V-shaped • If a< 0 the graph opens down (a is negative) • If a>0 the graph opens up (a is positive) • The graph is wider if |a| < 1 (fraction < 1) • The graph is narrower if |a| > 1

  7. To graph y = a |x - h| + k • Plot the vertex (h,k) (set what’s in the absolute value symbols to 0 and solve for x; gives you the x-coord. of the vertex, y-coord. is k.) • Use the slope to plot another point to the RIGHT of the vertex. • Use symmetry to plot a 3rd point • Complete the graph

  8. Graph y = -|x + 2| + 3 • V = (-2,3) • Apply the slope a=-1 to that point • Use the line of symmetry x=-2 to plot the 3rd point. • Complete the graph

  9. Do Now 10/12/2015 • Graph

  10. Graph y = -|x - 1| + 1

  11. Write the equation for:

  12. The vertex is @ (0,-3) • It has the form: • y = a |x - 0| - 3 • To find a: substitute the coordinate of a point (2,1) in and solve • (or count the slope from the vertex to another point to the right) • Remember: a is positive if the graph goes up • a is negative if the graph goes down So the equation is: y = 2|x| -3

  13. Write the equation for: y = ½|x| + 3

  14. Practice/Homework Worksheet: Graphing Absolute Value Functions Identifying Absolute Value Function equations Homework: Textbook P.71~72

More Related