1 / 9

Parametric and Inverse Functions

Parametric and Inverse Functions. Nate Hutnik Aidan Lindvig Craig Freeh. Intro Video. Defining a Function Parametrically. Parameter: Another way to define functions by defining the X and Y in terms of variable T. (x = t + 1) (y = t 2 + 2t)

allan
Download Presentation

Parametric and Inverse 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. Parametric and Inverse Functions Nate Hutnik Aidan Lindvig Craig Freeh

  2. Intro Video

  3. Defining a Function Parametrically Parameter: Another way to define functions by defining the X and Y in terms of variable T. (x = t + 1) (y = t2 + 2t) • Now say that t=2, then just plug the number 2 into each equation to get the x and y coordinates. They are (3,8) • The relationship can also be solved with substitution. Solve for t in terms of x. t = x - 1. Then plug that into the y equation. Then you end up with y = x2 - 1, which is the same as just solving for each point with t. • Tips: a graphing calculator can be used to graph it parametrically, it gives an x= and a y= to enter in the relationship of t.

  4. Inverse relations and functions Inverse relation: The ordered pair (a,b) is in a relation if and only if the ordered pair (b,a) is in it. Horizontal line test: We've heard of the vertical line test, so the horizontal line test simply test the first equation, so see if the inverse will be a function or not. The intial graph failed the horizontal line test, so the inverse that opens to the right failed the vertical test. Inverse is f-1

  5. Finding Inverse Algebraically • Simply switch the x's and y's, and then solve it again for y. Note the domain and range. x = y/y+1 Example x(y+1) = y multiply by y+1 xy + x = y distribute xy - y = -x isolate y y(x-1) = -x factor out y y = -x/x-1 divide by x-1 y = x/1-x multiply top and bottom by -1

  6. Inverse with reflections • The points (a,b) and (b,a) are reflections of across the line y=x. they both have inverses because they passed the horizonal line test.

  7. Verifying Inverse Functions Inverse rule: A function is an inverse if f(g(x) = x and g(f(x) = x. Example- f(x)=3x-2 g(x)=x+2/3 f(g(x) = 3(x+2/3)-2 = x+2-2 = x g(f(x) = 3x-2+2/3 = 3x/3 = x

  8. Examples Find the value of the parameter: x = 4t and y = t2 + 5 for t=2 x = 4(2) x = 8 y = (2)2 + 5 y = 4 + 5 y = 8 (8,9) Points can each be found like this..... or Take previous two parameters and make an equation of y in terms of x. t=x/4 y=(x/4)2 + 5 y = (x2/16) +5 ...either way works, and the same relationship is there.

  9. Examples (a) is it a function (b) is its inverse a function (a) yes, because it passes the vertical line test. (b) no, because it failes the horizontal line test.

More Related