Graph each function. See Examples 1 and 2. ƒ(x)=3|x|

Question

Accepted Answer

Hello everybody. How we're doing? All right. Today today we're gonna be looking at this math question that says for the following function sketch its graph where the function is F of X is equal to seven multiplied by the absolute value of X. Now the is provided are all four different graphs. A is a graph in the shape of a bean opening upwards with points at negative three comma 28 and positive three comma 28 with a vertex at zero comma seven. As your choice B is a graph in the shape of a V opening upwards with points at negative three comma 21 positive three comma 21 with a vertex at zero comma zero. That's choice C is a graph in the shape of a V opening upwards with points at negative 21 comma three and positive 21 comma three and a vertex at zero. Comma zero and D is a graph in the shape of a being opening upwards but starting below the X axis with points at negative three, comma 14 and positive three comma 14 and in a vertex of zero comma negative seven. So the first thing we gotta think about when approaching this question is what is the parent function here? So we have our parent function is the absolute value of X. So our graph should generally look like what the graph of the absolute value of would look like. And that graph is the shape of a V. So if you have, if you have the graph of absolute value of X, that will look like a V with the vertex at the origin zero comma zero and all the Y values will be positive because whatever X you place inside the absolute value bars because it's an absolute value that even the, if the X is negative, it will come out positive. And then we're multiplying it by multiplying it by seven and it's a positive seven. So that value will stay positive. So this graph is gonna open upwards towards positive Ys and it's going to remain always above the X axis to make sure every Y is positive. So with that knowledge, we can look at answer choice D and eliminate it right away because although it's opening upwards, it starts below the X axis. Its vertex is a zero comma negative seven which is a negative Y which we will not obtain. So now we can focus on answer choices A B and C A choice A and B look relatively similar but a choice C does not as choice C is a lot more stretched out the V is a lot wider. So we have to think about the points that they gave us and see if we can eliminate this any further before moving on to our work. So we see that a point that they gave us was negative 21 comma three. And we see that the V is a lot stretched out. So to reach a Y value of three, you had to go all the way to negative 21 or positive 21. So just by thinking about the equation that we have, we have F of X is equal to seven multiplied by the absolute value of X. So even if we put an X of one, we're already, we're multiplying that one by the seven and we're already gonna have a Y above three. So it'll be a Y of seven already for X is one. So looking at the graph of C where even at an X of three or at an X of negative 21 we're only at a Y of three, we can also eliminate that answer choice because it's stretched out a lot. And in our answer, since we're multiplying it by, by seven, we're actually gonna have a narrower V. So it's gonna be stretched higher, more vertical. So now between Entero A and B, we can start doing some work. So we have different points given to us, they both choose the X's negative three and positive three. So we can plug both of those in to check what point they give us as well as the vertex. So let's say let's pick negative three first. So we'll have F of negative three is equal to seven multiplied by the absolute value of negative three, which is seven multiplied by three, which equals 21 or the points negative three comma 21 because we plugged in negative three for our X and we received A Y of 21 and that matches up with answer choice B and does not match up with answer choice A. So we can already start turning towards answer choice B. Now let's test the other point that they gave us with an X of three. So we'll have F of positive three, that's equal to seven multiplied by the absolute value of positive three, which is equal to seven multiplied by three. Once again, which is equal to 21 or the 0.3 comma 21. And once again, that checks out with Aster choice B but does not check out with a choice A. And finally, as one last confirmation we can test for the vertex. And that happens at an X of zero for both graphs. So we can have F of zero equal to seven multiplied by the absolute value of zero, which is equal to seven multiplied by zero, which is equal to zero or a vertex at zero comma zero. And once again, that checks out with answer choice B so we can confidently say that answer choice B is the correct graph and the answer to our question. So I hope that was helpful. And until next time.

Graph each function. See Examples 1 and 2. ƒ(x)=3|x|

Key Concepts

Absolute Value Function

Vertical Stretching of Functions

Graphing Piecewise Functions

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