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Sketch the graph of the line $x-2 y+1=0$ on the same axes as the graph of $y=f(x)$ from Exercise $18 .$ How many points of intersection do you see? What are their coordinates?

$$\text { Three; }(1 / 5,3 / 5),(7 / 3,5 / 3),(11 / 3,7 / 3)$$

Algebra

Chapter 1

Functions and their Applications

Section 3

Applications of Linear Functions

Functions

McMaster University

Baylor University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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(a) Sketch the graph of th…

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Points of laterseetion Gra…

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Use graphing to find the p…

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Find the points of interse…

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Graph $y=x^{3}-x^{1 / 3}$ …

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Find the coordinates of th…

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$15-18=$ Finding Intersect…

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Okay. Working with piece wise functions, we're gonna be determining where a linear function intersex this piece wise function. You can see graft and yellow. The piece of eyes function given us F of X is equal to negative two x plus one If X is less than or equal to one two x minus three if one if X is greater than one and less than or equal to three and negative X plus six. If X is greater than three, we're gonna be graphing. The function given in blue X minus 21 plus one is equal to zero. Bring this into slope intercept form to make it easier for graphing see adding to wider both sides. Where we get X Plus one is equal to two y dividing both sides by two. We end up with one half X plus one half is equal. Why that gives a slope intercept form. If you were to graph this, it would look something like this. You can either plug that into a graphing calculator. All of these functions here do it by hand. However you would like next. What we want to do is figure out all of these points of interception here. To do that, we could either again do it graphically on a graphing calculator. Or we could set our function in blue equal to each one of our piece wise functions. And that's what we're gonna do to start. So let's do negative two x plus one, setting that equal to one half X plus one half solving for X. Here we end up finding that X is equal to 1/5 and plugging 1/5. I'm sorry. There we go toe 1/5. And if we were to plug 1/5 back into our piece wise function, we would find that why, in this case is equal to 3/5 that gives us one of our points of intersection. Next, we can take our second piece to X minus three. Set that equal to our linear function one half x plus one half you were to solve for X You would find here that X is equal to seven thirds and plugging seven thirds back into this equation, we would find that we have a Y equal to five thirds, giving us our second point of intersection doing the same process again. But with the third piece of our piece Wise function, having negative X Plus six and setting that equal to one half X plus one half solving for X will find that X is equal to 11 3rd and plugging 11 3rd back into the piece Wise function. We find that why is equal to seven thirds giving us our third point of intersection right there.

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