In Exercises 39–50, graph the given functions, f and g, in the sa...

Question

In Exercises 39–50, graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x)= |x|, g(x) = |x| +1

Accepted Answer

Welcome back. I am so glad you're here. We are given two functions. The first is F. Of X. Which is equal to the absolute value of two X. And the second function is G of X. Which is equal to the absolute value of two X. Again now plus five. And we are asked to graph these two functions and then describe the relation between the two functions on our graph. So I am going to draw a horizontal X. Axis and a vertical Y axis which meet together at the origin in the middle. And now we're ready to graph if you know what the absolute value of two X looks like on a graph. Wonderful. If you don't you can always plot a few points to see what's going on. I'm going to choose 10 and negative one for some X values and then figure out the corresponding Y values and then plot those points on our graph. So plugging in one for X. That's the absolute value of two times X. But now times one. So two times one is two. So we've got the absolute value of two which is to looking at our graph starting at the origin, we're going to move to the right one unit for our X value and up two units for our Y value which is approximately here. Right now solving for X equals zero. That's the absolute value of two times not X but zero and two times zero is zero. So we've got the absolute value of zero which is zero and that's right at our origin here. Alright now solving for X equals negative one. That's the absolute value of two times negative one and two times negative one is negative two. So we've got the absolute value of negative two which is positive two. Looking at our graph, we're going to go to the left one unit for our X value. And we're going to go up two units for our value of two. For why? Now we can connect those dots. We know that as our X values would get larger that are Y values will also get larger. And as our X values head toward negative infinity are Y values will be heading toward positive infinity. So our F. Of X looks something like this. All right. How about R. G of X? Well, our G of X is almost identical to our F. Of X. They both have that absolute value of two. X. Going on. The only difference is that that G. Of X has plus five because the plus five is not happening directly to the X. It's not inside that absolute value bar. It's a vertical shift. So it's not happening directly to the exodus of vertical shift. And in this case because we are adding five, the vertical shift is going to go up five units. So that means instead of converging here the origin it's going to go across the Y axis at five. A value of Y equals five still zero for the X value. And then other than that it's going to look exactly the same as our F of X. Because the only difference was that shift going up five. So there's our G of X. Okay. So we've graphed are two functions and now describing the relation between both graphs, well, G of X is the same as F of X. Except G of X is going to shift five units upward. Alright, so that's what we've got. Now. Let's look at our answer choices to see what matches for answer choice. A. The graph of G is the same as the graph of F. Yes, shifted five units upwards. Yes, that's what we've got and it looks like our graphs match. That's wonderful. Let's check really quick with the other ones to see if perhaps we've missed something in our graph. So let's look at answer choice B. That says the graph of G is the same as the graph of F. Yeah, shifted five units downwards, nope. We shifted five units upwards. Not downwards. Alright, let's go check out see see says the graph of G is the same as the graph of F. Yes, shifted five units downwards again, nope. We shifted upwards and look at this graph this graph has our functions pointing down and that's not what we had. All right. Let's check answer choice. D. D says the graph of G is the same as the graph of f shifted five units upwards. Well, yeah, that is what we had. What does that graph look like? My graph is not going to go on to the second page here, but okay, that one they're pointing down instead of pointing up, so this one does not work. Therefore, answer choice A was our winner. Well done. We'll catch you on the next one.

In Exercises 39–50, graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x)= |x|, g(x) = |x| +1

Key Concepts

Absolute Value Function

Vertical Shifts

Graphing Functions

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