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

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) = x³, g(x) = x³ +2

Accepted Answer

Welcome back. I am so glad you're here. We are given two functions. Were given F of X equals three X cubed. And we are given G of X which equals three X cubed again minus seven. We are to graph both of these functions and then to describe the relation between the two functions on our graph, I'm going to draw a coordinate plane here with a horizontal X axis and a vertical Y axis. They meet together at the origin in the middle. Now to graph our F. Of X. If you've got three X cubed memorized and know exactly how it goes on the graph. Wonderful. If you don't know exactly how it goes, you can always plot a few points to see what's going on. I'm going to choose three values for X 10 and negative one. Figure out their corresponding Y values and then plot those points on the coordinate plane. So plugging in 114 X three not times X. But now three times one cubed. Well, one cubed is one. So this three times 1 equals three. We look at our coordinate plane starting at the origin 00. We're going to go one to the right for our X value and we're going to go up three for our Y value which is approximately here. Now substituting zero for X. That'll be three times zero cubed. Well zero cubed is zero. So this is three times zero which is zero. That's right at the origin. We can draw a dot right at 00 at the origin. Now for X equals negative 13 times negative one cubed. Well negative one cubed is still negative one. So we've got three times negative one which is negative three. Starting at the origin we're going to go one to the left for our X. Value and then down three for our Y value. And so this we've got these three points and there's actually going to be a bit of a curve. If you really needed a specific um graph that you need to plot, you can plot points in between zero and one. You can do one half but this is going to end up looking approximately like this ish. And we'll label that F of X. Alright, we've got one of them done now for G of X. Well G of X is very similar to F of X. They both have the three X cubed but this G of X has this minus seven here. That minus seven is not occurring directly to the X. The minus seven is not also being cubed. So we know that that indicates a vertical shift because it's not happening directly to the X. And the shift that's taking place here because it's vertical and it's subtracting seven is that we are going to go down seven units. So where f. of x intercepted the origin at 00 G of X is going to intercept the y axis at negative. seven but still zero for the X value. So that's somewhere down here. And so then this graph will otherwise be identical to our F of X. Because the only difference was that minus seven But it'll be down seven units. So it asks us to describe the relation between both graphs, they are going to be the same as each other except shifting seven, shift 7 units down. All right now, let's look at our answer choices. See if we get a match for answer choice. A. The graph of G. S the same as the graph of F yes, shifted seven units upwards, nope not shifted seven units upwards. Alright, let's check out. B B says the graph of G is the same as the graph of F. Yes, shifted seven units downwards. Yes, that looks correct. Let's look at our other two answer choices to see if we perhaps missed something. The graph of G is the same as the graph of F. Yes, that's good for answer Tracy, shifted seven units to the left, nope, not to the to the left. And let's look at answer choice. D. The graph of G is the same as the graph of F. Yes, shifted seven units to the right, nope, not to the right. We went down so the correct answer here is answer choice. B. 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) = x³, g(x) = x³ +2

Key Concepts

Graphing Functions

Transformation of Functions

Coordinate System

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