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Evaluate $ f(-3) $ , $ f(0) $ and $ f(2) $ for the piecewise defined function. Then sketch the graph of the function.

$ f(x) = \left\{ \begin{array}{ll} 3 - \frac{1}{2}x & \mbox{if $ x < 2 $}\\ 2x - 5 & \mbox{if $ x \ge 2 $} \end{array} \right.$

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$\frac{9}{2}$$,3,-1$

01:48

Jeffrey Payo

03:20

Heather Zimmers

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 1

Four Ways to Represent a Function

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Khushi G.

March 3, 2022

if f(3)=5 and f is a linear function find the value of f inverse 5

Lina B.

March 18, 2022

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May 13, 2022

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Missouri State University

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

04:31

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

02:32

Evaluate $ f(-3) $ , $ f(0…

04:08

02:09

02:43

Evaluate $f(-3), f(0)$, an…

04:41

Evaluate $f(-3), f(0),$ an…

04:39

02:18

02:47

02:33

02:22

00:55

Evaluate the piecewise def…

01:24

Graph the piecewise functi…

02:00

Given the function defined…

00:36

Sketch the graph of $f$

all right here we have in blue a piecewise function. And our goal is to find some points and to grab the function. So let's start and look at the points. If I want f of -3, I have to pay attention to which part would include ministry and that would be the top part. So I can plug in minus 34 acts. I'll get three minus one half of minus three. That's double negative three plus three halves. Um and then that becomes 9/2, So that's one of our points. We can plot it as we go f of -3 Should be 9/2, which is 4.5. So something like, Like they're 4.5. Okay, so the next point of interest is F0 And I check again and we're still looking at the top part because X is less than two. So we'll plug into that part of the function. So 3 -1 half of zero, which is just three. So f of zero is 3. So we can plot that point and While we're at it we can see we have a line and we're going to go till two. So when I'm about to reach to basically in the limit, As X approaches two from the left side, then I will plug in two for my ex And I'll get three one half of two. So that's what I'm approaching. But notice there's no equal sign on the top part, Therefore 3 -1 equals two. That means I'm gonna have a whole at to the limit there exists on the left side but I'm going to have a hole here so I As I approach to then the whole is at two. So this will be a whole and I'll try to draw a line then connecting there. Okay so that's kind of the left side. Um Up until to now notice um Now we're gonna get and we're going to take a look at the bottom half here, this is for X. Greater than or equal to two. So let's find out what happens when we plug into. So that will give us twice two minus five. 4 -5 is -1. So at two we're actually skip all the way down to -1. And at this point since we've already done three points let's go ahead and just draw the rest of the graph, let's just get one more point. We know it's a line. Let's do um How about f. f. 4? That will be twice four minus 58 minus five is three. So at four we're up at three, something like this. Let's make it a line and I think we've done everything we need to do is draw the graph, we found some points using our piecewise. Alright hopefully that helped to have an amazing day

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