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

Write the different transformations. Use the drive given graph using the graph of F of X equals the absolute value of X. Also write the equation for the graph. Now we got us here, we have an absolute biograph that's pointed downwards. Now, the original function I I mentioned is an absolute value graph. So beforehand, this would look the graph that starts at the origin and expands up to the right and up to the left with a sharp corner in the very middle of the vertex. And we have four possible answers for this all with different transformations. A couple of them reflect over the X reflect over the Y, all of them have some kind of shift. And were given the equation at the very end. Let's see if we can determine what our transformations are. So the normal absolute value graph starts with a vertex at 00. Now we notice here our new vertex is moved, we actually moved up by five units and left by three hits. Those makeup are shifts have a shift up five and a shift left by three. Now I also mentioned that this is pointed downwards earlier, we have a reflection. Since we are now pointing downwards, this reflection is over the X axis. We can now use this to form an equation. Now reflection over the X axis means we're going to multiply everything by a negative number, you'll say negative. Now we have our absolute value, we're shifted to the left by three. So what we have the absolute value of X plus three and we are also shifted up by five. So we will add five at the very end. So we have Y equals the negative absolute value of X plus three plus five. It has a shift up five shift left three and reflection over the X axis, which means the answer to our problem turns out to be answer A OK. I hope to help us 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.

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