Consider the following nonlinear system. Work Exercises 75 –80 in...

Question

Consider the following nonlinear system. Work Exercises 75 –80 in order.y = | x - 1 |y = x^2 - 4How is the graph of y = | x - 1 | obtained by transforming the graph of y = | x |?

Accepted Answer

Hello everybody. I hope you're doing all right. Today today we're going to be looking at this math question that states describe the transformation required to draw the graph of Y equals the absolute value of X minus three from the graph of Y equals absolute value of X. Now the answers provided are a shift. The graph of Y equals absolute value of X three units up B shift the graph of Y equals absolute value of X three units down C shift the graph of Y equals absolute value of X three units to the right and D shift a graph of Y equals absolute value of X three units to the left. Now, I see that the graph they're providing us is Y equals absolute value of X minus three. And now I have to think about different rules that we have for transformations of graph in a general formula is Y equals A. And I'll write this uh in regards to an absolute value equation. So we'll have a absolute and then an absolute value bar and inside of it X minus H then close the absolute value bars and outside we have plus K. So we have to compare this to the equation that we have. In our case, we don't have an A so that will cancel out and we don't have a plus K so that will cancel out. So we're only having a Y equals absolute value of X minus H. Now, the rule in this case is if H is greater than zero, the graft will shift, right? And if H is less than zero, the graph will shift left. Now you have to think about it. Yeah, I, we, we know there's an X minus H. So when we talk about if H is greater than zero, we do not take that negative in front into account, we are only looking at the H. So if, let's say in in our case, we have X minus three, we are only focusing on the three. So the three, it's greater than zero and R three is equal to H. So therefore we have a shift right? And in this case, we have a three. So it will be three units. So this graph will have a shift to the right of three units or in this case, answer choice C. So I hope that was helpful. And until next time.

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Consider the following nonlinear system. Work Exercises 75 –80 in order.y = | x - 1 |y = x^2 - 4How is the graph of y = | x - 1 | obtained by transforming the graph of y = | x |?

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