In Exercises 1-16, use the graph of y = f(x) to graph each functi...

Question

In Exercises 1-16, use the graph of y = f(x) to graph each function g.

Graph of y = f(x) showing a horizontal line segment from (1, -3) to (4, -3).

g(x) = f(x)+1

Accepted Answer

Hello, today we're going to be graphing G of X as a transformation of F of X. So what we are giving is why is equal to F of X and we are told that G of X is going to equal to F of X plus two. Now we don't know what F of X is. However, we are given the graph of F of X which is going to be the straight line whose endpoints are at one comma negative three and four common negative three. So let's go ahead and figure out the transformation we need in order to go from Y two G of X C G of X has one similarity and they both involve the function of F of X. However, in G of X where adding two to F of X. So that means that G of X is in the form of F of X plus que and K is going to be a vertical shift of this graph. See whenever you're adding a value to a function, that means that you're going to have a K value, which in this case involves one transformation which is a vertical shift. And since K is equal to positive two, we're going to have a vertical shift of the graph f of X two units up. So that's gonna be the only transformation that we need. And that means that for every point on this graph, every point is going to go up two units. Or in other words, we're adding two to the Y values of the endpoints. So if we're looking at our first endpoint, we have one common negative three. If we shift this endpoint up two units, that means we're going to add two to the Y value of this endpoint. And that means that the new point for G of X is going to be one common negative one. And for the other end point which is four comma negative three, we're going to do the same thing where we're shifting this point up two units. So we're going to be adding two to the Y value which gives us the new end 20.4 comma negative one. So that means that the new graph for Y is equal to F of X is going to be shifted up two units where the new endpoint is at one common negative one and the other endpoint is going to be at four comma negative one and that's going to be G of X. And the graph that accurately represents this is going to be C as C has the endpoints of one comma negative one and four comma negative one. Which indicates a vertical shift of two units up. So I hope this video helps you understand how to graph using transformations. And I'll go ahead and see you all in the next video.

In Exercises 1-16, use the graph of y = f(x) to graph each function g.
g(x) = f(x)+1

Key Concepts

Function Transformation

Graphing Functions

Horizontal and Vertical Lines

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