Defining piecewise functions Write a definiti...

Question

Defining piecewise functions Write a definition of the function whose graph is given

Accepted Answer

Welcome back everyone to another video. Determine the function for the following graph. So we're given the graph of a function, and as we can see, it basically consists of two lines. We have a horizontal line and we have to recall that horizontal lines can be defined as y equals A, where A is a number. And in this case, because there's a horizontal line that crosses the y axis at the value of 5, we can say that this. Part of the graph corresponds to Y equals 5. Now, what can we see? Well, essentially this part of the function extends towards negative infinity on the left and on the right, it extends towards the value of 1 at X, right? So we can say that this part of the function essentially corresponds to Y equals 5 for X, less than or equal to 1. Now it doesn't matter if we say less than or equal to 1 or less than 1 because one is a common value for the two parts of the graph. We can then see another line which starts at X equals 1 and Y equals 5, right? So essentially we're just going to assume that the first line, which is the horizontal line, Essentially is defined at X equals 1 as well. Now, for the second line, which It is defined as y equals MXx plus B. It has a slope. We're going to say that this part of the graph is defined for x values that are greater than 1, and now we want to identify the equation of that line, and we can do that by finding the slope and the y intercept. So what we can do is basically take two points to find a slope. Now, slope M is equal to the change in Y divided by the change in X. And we can take two Y values. Let's take Y of 11, and then we're going to take Y of 5. So the slope is going to be equal to 11 minus 5, divided by the change in X. So basically at 11, we have the X value of 3. And at 5 we have the X value of 1. So 11 minus 5 gives us 66 divided by 2 gives us a slope of 3. And now for the Y intercept, we can see that B is equal to Y minus MX. We can take any point we want. Let's let's say that we are taking the common point which is X equals 1, Y equals 5, right? So 5 minus 3 multiplied by the value of X, which is 1, and this gives us the Y intercept of 2. Now once again, we, we said that X is greater than 1, but technically we can see that for the given line we can also take X equals 1 because it is the common point for the two parts of the graph. So now we have the two required functions to define the overall function. So the overall function F of X is a piecewise function. Such that we have Y equals 5, so, we're just saying 5, if X is less than or equal to 1, and it is equal to MX plus B where M is 3. And B is 2 if X is greater than 1. So we have our final answer. Thank you for watching.

Defining piecewise functions Write a definition of the function whose graph is given <IMAGE>

Key Concepts

Piecewise Functions

Domain and Range

Graph Interpretation

Watch next