Graph each function. See Examples 1 and 2. h(x)=|-(1/2)x|

Question

Accepted Answer

Hello everybody. I hope we're doing. All right. Today today we're gonna be looking at this math question that's at telling us for the following function sketch its graph where the function is F of X is equal to the absolute value of negative 1/5 multiplied by X. Now the estis that they provide us are a, a graph in the shape of a V opening upwards with points negative 5 15 comma three and positive 15 comma three with a vertex at 0.0. As choice B is a graph in the shape of A V opening downwards with the points negative 15, comma negative three and positive 15 comma negative three with the vertex at zero, comma zero answer choice C is a graph in the shape of a V opening upwards with the points at negative 15 comma 15 and positive 15, comma 15, invert text at zero, comma zero. And as choice D is a graph in the shape of A V opening downwards with the point at negative 15, comma negative 15 and positive 15 comma negative 15 and a vertex at zero comma zero. Now, when looking at this question and the equation that we have, we see that we have an absolute value equation. This means that anything that you take out of anything within the absolute value bars will become positive. Once you take them out of the absolute value bars, even if the answer you get is negative. Once they have because of the absolute value bars, it would just turn positive once you take it out. Therefore any answer for A X for our function will be positive. So we won't have any negative Y values. So right away, we can eliminate any graph that has negative Y values any graph that's opening downwards below the X axis. So by looking at our answers, we can eliminate choice B which has a graph opening below the X axis. And we can also eliminate answer choice D which also has a graph in the shape of a V opening downwards below the X axis. So now we're left with two answer choices, answer choice A and then choice C. So we see that they both use the points negative 15 with an two points with the XS at negative and one with the X at positive 15. So we can test those points and see what we obtain for A Y and see where that point will lie. So let's do exactly that. First, let's try F of negative 15. So have F of negative 15 is equal to the absolute value of negative one. This multiplied by negative and negative 1/5 multiplied by negative 15, the negatives will cancel out. So the answer will be positive anyways. And then you would have the absolute value of divided by five which will be three or the point negative 15 comma three. So that checks out with answer choice A but not with answer choice. C So now we tried the other point of where we have an X of positive 15. So we would do F of positive 15. So F of 15 is equal to the absolute value up negative 1/5 multiplied by positive 15. So we would have almost the same thing. We, we, we would now have negative 1/5 multiplied by is the same as saying the absolute value of negative divided by five. And that would be equal to the absolute value of negative three, which is positive three or the 0.15 comma three which once again checks out with a choice A but does not with a choice C. So we can confidently say now that answer choice A will be the answer to this question as it has the correct graph. So I hope that was helpful. And until next time.

Graph each function. See Examples 1 and 2. h(x)=|-(1/2)x|

Key Concepts

Absolute Value Function

Linear Functions

Graphing Techniques

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