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).

e. 𝔂 = ƒ( x ) - 4

3

Accepted Answer

Hello there. Today we're gonna 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 of X divided by 4 minus 5? Awesome. So it appears for this particular prompt we're asked to take our original function, which is Y equals F of X, and we're trying to describe the transformation. We're trying to describe what happens when Y equals F of X transforms to become Y equals f of. X divided by 4 minus 5. So ultimately what we're trying to solve is we're trying to figure out a way to describe what happens when this transformation occurs. So now that we know what we're ultimately trying to solve for, 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 stretched horizontally by a factor of 4 and shifted 5 units downward. The graph of F of X is stretched horizontally by a factor of 4 and shifted 5 units upward. C is the graph of F of X is compressed horizontally by a factor of 4 and shifted 5 units downward. And finally, D is the graph of F of X is compressed horizontally by a factor of 4 and shifted 5 units upward. Awesome. So, first off, let us know once again that our given function is Y equals F of X divided by 4 minus 5. And we now need to, in order to help us solve for this problem more effectively, we need to analyze each part separately. So let's focus our attention on the F of X divided by 4 part first. So we need to note and recall that this expression F of X divided by 4 matches the form of F of X divided by C. So once again, F of X divided by 4. Matches the form of F of X divided by C, which, as we should recall, will indicate a horizontal stretch by a factor of C. And because for this particular brown, we're told that C is equal to 4 because it's X divided by 4, so that means C is equal to 4. That will mean that the graph of F of X will be stretched horizontally by a factor of 4 units. Fantastic. So, once again, so it's gonna be stretched. So let's make a note of this, so it's gonna be stretched. And I'll do a capital H for horizontally, so it's gonna be stretched horizontally by a factor of 4. Fantastic. So now moving on to our second part that we need to analyze, which is the minus 5 part. So we need to note that the minus 5 at the end of the following, or the end of the I should say at the end following our F of X divided by 4. This means that it's in the form of F of X plus k, where this k value is going to be minus 5 or. 5. So that means that there will be a vertical shift by K amount of units. So it's important to note, as we should recall, that if K is greater than 0, that will mean that the graph of F of X will be shifted K units upward. Which I tend an arrow pointing up to mean upward. However, if K is less than 0, that will mean that our graph of F of X will be shifted, the absolute value of K, where these absolute value symbols mean, even if there's a negative value of K, it's going to be positive. So, for the condition where K is less than 0, that means that this graph of F of X is going to be shifted the absolute value of K units downwards, which I used an arrow pointing down to indicate downwards. So that will mean, considering the information that we just stated, that sense K is equal to -5, that means it is less than 0. So that means that the graph of FF X is going to be shifted 5 units downwards. So I put a 5 with an arrow pointing down, so it's going to be shifted 5 units downwards. So that means, considering all the information that we discovered together, the final answer without a doubt. Has to be multiple choice answer letter A because therefore the graph of F of X will be stretched horizontally by a factor of 4 and shifted 5 units downwards and as a states, the graph of F of X is stretched horizontally by a factor of 4 and shifted 5 units downward. And that's it. We've officially solved for this problem. 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).

e. 𝔂 = ƒ( x ) - 4
3

Key Concepts

Vertical Shifts

Function Notation

Graph Transformations

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