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

Question

Accepted Answer

Hello everybody. Everything. All right. Today today we're gonna be looking at this math question that states for the following function sketch its graph where the function is F of X is equal to negative seven multiplied by the absolute value of X. Now the choices that they provide us are four different graphs with S choice A being the graph in the shape of A V opening upwards with the point with a point at negative three comma 28 A vertex at zero comma seven and another point at three comma 28 choice B has points at negative three comma 21 and positive three comma 21 enter vertex at zero, comma zero as a choice C has points at negative three comma negative 21 and positive three comma negative 21 in vertex at zero comma zero and answer choice D has points at negative three comma negative 28 and positive three comma negative 28 with a vertex at zero comma negative seven. Now, the first thing we should think about when, before we even start is what would this graph look like? So we know we have the absolute value of X and the A negative seven in front of that. So the negative seven is not included within the absolute value bars. So it's multiplying whatever comes whatever X comes out of those absolute value bars. So normally when you have a graph of an absolute value, that graph would be in the shape of a V opening upwards because whatever is inside the absolute value bars would be positive. And if it's positive, that means you're not gonna have any negative Ys, therefore, it would be above the X axis X axis. However, because the negative seven is outside those absolute value bars, whenever you bring out a positive value outside of those absolute value bars, they'll be multiplied by a negative number. So instead of that answer always being positive, it will not always be negative. So we're flipping it instead of being above the X axis. Now it's always gonna be below the X axis. So with that in mind, we can eliminate answer choices a NB right away because they both have, have a graph in the shape of a V opening upwards above the X axis. So those Ys will be positive and we want them to be negative in this case. So now we turn our attention, the answer choice is C and D. So to test your points, all we have to do is test different values for our equation. So for example, they have a point at negative three. So let's test negative three. All we do is plug in negative three for our X. So we'll have F of negative three is equal to negative seven multiplied by the absolute value of negative three, which is the same as saying negative seven multiplied by positive three, which equals negative 21. So this would be a point of three comma negative 21 or negative three comma negative 21 because we plugged in negative three for our X. So that checks out with reso C does not check out with asteroid D. So we continue now we want to test our origin, our vertex. So for this, we'll do F of zero since they both have an X at an X point at zero to see what the Y would be. So F of zero is going to be negative seven multiplied by the absolute value of zero, which is just negative seven multiplied by zero, which is equal to zero or the 0.0 comma zero, which again checks out with choice C but does not check out with answer, answer choice D. And finally, we'll test out the last point they gave us which both graphs have a point at an X of three. So we'll do F of three. So F of three is equal to negative seven multiplied by the absolute value of three, which is the same as saying negative seven multiplied by three, which is 21 or negative 21. In this case, So we'll have negative seven multiplied by positive three will be negative 21 or the point three comma negative 21 which once again checks out with choice C but does not check out with Ancho D. So we can confidently say that the graph for answer choice C is the correct graph and will be the answer for a 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 Stretch and Reflection

Graphing Piecewise Functions

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