Each of the following graphs is obtained from the graph of ƒ(x)=|...

Question

Each of the following graphs is obtained from the graph of ƒ(x)=|x| or g(x)=√x by applying several of the transformations discussed in this section. Describe the transformations and give an equation for the graph.

Accepted Answer

Correct the different transformations used to draw the given graph piece in the graph of F of X equals absolute value of X. Also write the equation for the graph. Now to graphic transformations, we first need the base graph F of X equals the absolute value of X. This is a graph that starts with the origin goes up into the right and up into the left. The first thing we notice is our new graph is flipped downwards. So we have a flip over the X axis. Now we also noticed we have horizontal and vertical shift horizontally. Our new portion point for the graph moves to the right two and down for it. So we say right, two units and down four units, we can now form a graph from our base graph. We have F of X equals a flip over the X axis implies a negative in front of abs of value, we now have a shift to write two units. So inside the bars with our X, we'll put a minus two. Finally down four units on the outside of these bars, we will put minus four a breath if F of X equals negative absolute value of X minus two minus four. This corresponds with answer D OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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Each of the following graphs is obtained from the graph of ƒ(x)=|x| or g(x)=√x by applying several of the transformations discussed in this section. Describe the transformations and give an equation for the graph.