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Consider the function given by$$f(x)=\left\{\begin{aligned}-2 x+1 & \text { if } x \leq 1 \\2 x-3 & \text { if } 1 < x \leq 3 \\-x+6 & \text { if } 3 < x\end{aligned}\right.$$Find $f(0), f(1), f(2), f(3)$ and $f^{5}$ ). Plot the graph of $y=f(x)$

$$1,-1,1,3,1$$

Algebra

Chapter 1

Functions and their Applications

Section 3

Applications of Linear Functions

Functions

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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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03:26

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given here is a piece wise function which we're going to be using to find several points on a graft. Ultimately, graph the peace fights function. Let's start by finding f of zero, noting that zero satisfies the condition of our first piece here being that it's less than or equal to one, and finding this will plug zero into that piece of our equation. Negative too. Times X, which in this case is zero plus one, give us a value equal to one for f of one. This will also be satisfying the first piece of our function, considering that one is equal to one which satisfies the condition of being less than or equal to one. Plugging that into our equation, we get that f of one is equal to negative. One f of two is gonna be satisfied. The second piece of our equation, considering that follows between one and three being greater than one in less than or equal to three plugging to into that piece into two x minus three, we get that it's equal to one f of three is again gonna fall into that same second piece plugging three and two times three minus three. We get a value equal to three and f of five satisfies the third piece of our function. Being that five is greater than three plugging five and do our equation, we get negative five plus six, which gives us the value of one. We can now plot each of these points on our graph to get a feel for what this function looks like graphically plotting her first point of 01 goes right here. One negative one right here to one, 33 and 51 It gives us a graph that looks like this, and that's how you would graph it.

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