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Figure $5(b)$ shows the graph of a piecewise linear function $f$ Find the algebraic formulation of $f(x)$. Find $f(-1), f(1.5),$ and $f(4)$

$f(x)=\left\{\begin{array}{cc}2 x-1 & x \leq 1 \\ 1 & 1<x \leq 2 \\ x-1 & x>2\end{array}\right.$$f(-1)=-3, f(1.5)=1, f(4)=3$(Either end points may have equality in 14 and $15 .$ )

Algebra

Chapter 1

Functions and their Applications

Section 3

Applications of Linear Functions

Functions

Campbell University

Oregon State University

Idaho State 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).

03:18

04:51

Figure $5(a)$ shows the gr…

03:47

Figure $5(\mathrm{c})$ sho…

01:25

For the piecewise linear f…

Write the linear function …

03:11

(a) write the linear funct…

02:20

Writing a Linear Function.…

02:25

$5-14$ . Suppose the graph…

01:30

02:31

Work each problem related …

02:42

In Exercises 11–14, (a) wr…

00:35

Find the slope of the grap…

using piece wise functions, we wanna find what the graph with the function of FX's. Given the graph of F X that we have here to start, we'll split each of our line segments up into three parts A, B and C. We want to find the individual functions for each one of those linear lines, starting with point A. We can plug in our to coordinate points to find its slope into our soap formula listed at the top. In doing so, we find that segment a has a slope equal to two. Then plugging that slope and one of the coordinate points into our point slope form, we find that a has a function which is equal Thio, why equal to two X minus one. Looking at the bounds we have here, we find that it is going to be X is less than or equal toe one. We find that because we can see that on our graph. We have X is equal toe once and right at this point. So for anything less than that, extending down to here further actually, to infinity, that would apply for Segment B. Using our soap formula, we find that we have a slope equal to zero plugging that and one of the coordinate points into our point slope form. We find that we have a function equal to one, and that would be for the bounds of if X is greater than one, but less than or equal to two again. That's because we're looking at our two points here and here. One and two got to sit somewhere within that. For see, we find that we have a slope equal to one, a function equal to X minus one, and that is applicable if X is greater than two again because we have to hear and it's for anything greater than it on the X axis. Now we can fill in our piece. Wise function as F of X is equal to x oops as X F of X is equal to two x minus one and that if X is less than or equal to one, F of X is equal to one. If X is greater than one, but less than or equal to two, and that f of X is equal to X minus one. If X is greater than two. Suppose we wanted to check this out and fucking a couple values. So if we're looking at X is equal to negative one that tells us that it's got that we have to be using our first function function A because X is less than or equal to one. Doing that plugging negative one into two X minus one. We get that that value is equal to negative three. If X were equal to 1.5, we know that that's gonna fall within our second equation equation be because 1.5 lies within the bounds of greater than one, but less than or equal to two. Plugging that in, we find that it is equal to one. And if X is equal toe Ford, we know that we're gonna be using our third equation equation. See function, See, because four is greater than two plugging that in, we have four minus one equal to three

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