Describe how each graph is obtained from the graph of 𝔂 = ƒ(x...

Question

Describe how each graph is obtained from the graph of 𝔂 = ƒ(x).

a. 𝔂 = ƒ(x - 5)

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Given the function Y equals F of X, which transformation describes the graph of Y equals F X + 4? Awesome. So it appears for this particular prompt we're asked to examine our original function, which is Y equals F of X, and we're trying to describe how to we're trying to figure out a way to describe how this original function F of X transforms when it turns. Y equals F of X + 4. So what happens when our original graph, which is Y equals F of X, transforms to be Y equals F X + 4. So that's what we're ultimately trying to solve for is what kind of transformation is taking place. So, let's read off our multiple choice answers to see what our final answer might be. A is the graph of F of X is compressed horizontally by a factor of 4. B is the graph of F of X is shifted 4 units to the right. C is the graph of F of X is shifted 4 units to the left, and finally D is the graph of F of X is stretched horizontally by a factor of 4. Awesome. So first off, let us note that Y equals F of X + 4 is in the form of Y equals F of X plus H. So let us note that for a given function of F of X, as we should recall, a transformation of F of X plus H will shift the graph horizontally by H amount of units. So let us know, as we should recall that if H is greater than 0, that would mean that the graph of F of X will be. Shifted H amount of units to the left, which I'll put a capital L in quotation marks to indicate left. So once again, if H is greater than 0, that means the graph of F of X will be shifted H amount of units to the left. However, if H is less than 0, that will mean that this graph of F of X. Will be shifted the absolute value of H, which, as we should recall, the absolute value of anything inside of the absolute value symbols, it's going to mean that it's going to be a positive value. So even if it's a negative value of H, it will still be positive. So that will mean, as a result that when H is less than 0, this graph of F of X will be shifted the absolute value of H units to the right, which I put a capital R in quotation marks to represent right. So with that said, keeping this piece of or pieces of information in mind, we need to note that our given function states that H, in this case, since we note that Y is equal to F of X + 4, that means that H is going to be. Equal to 4, which means as a result that H is greater than 0. And because H is greater than 0, therefore, without a doubt, the graph of F of X will be shifted 4 units to the left, which means that our final answer has to be multiple choice answer letter C. And once again, C states that the graph of F of X is shifted 4 units to the left, and that's our final answer. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Describe how each graph is obtained from the graph of 𝔂 = ƒ(x).

a. 𝔂 = ƒ(x - 5)

Key Concepts

Function Transformation

Horizontal Shifts

Graphing Functions

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