Solve each problem. A graph of y=ƒ(x) is shown in the standard...

Question

Solve each problem. A graph of y=ƒ(x) is shown in the standard viewing window. Which is the only value of x that could possibly be the solution of the equation ƒ(x) =0? A. -15 B. 0 C. 5 D. 15

Graph of a line in a standard window with x and y axes from -10 to 10, showing a positive slope.

Accepted Answer

Hello, everybody, everybody. All right. Today, today we're gonna be looking at this math question that says, consider the graphs shown which of the following val values of X is most likely the solution of the equation G of X equal to zero. And they provide us for the graph that has a negative slope. So it's angled downwards where Y is equal to G of X. And they don't provide us with any points along that graph. Now the answer choices that they give us are a negative 12, B zero C six and D positive 12. Now we can look at the graph that they gave us and just try to label some of the lines a little better. So on the Y axis, we see that each line is gonna represent two units. So we can label the first line as two, second line is four, third line, as 6/4 line as eight. And the final line is labeled for us as 10. And then on the X axis, we see that each one of them goes by one unit. But once again, let's just label the two, the four, the six and the eight. So it's a little, a little easier for us to keep track of it. Now, what they're asking us is when will G of X equal to zero? So when will we have a Y value of zero? For, for what X? That's, that's what they're asking. They're asking for what X will Y equals zero. So we have to find the X value that will give us a Y of zero and we can do that by looking at the graph and looking at our line. So looking at our answer choices, one of the answer choices in ze- is zero. So add an X of zero and we can simply look at our graph at an X of zero. We see that our graph connects on the Y axis at six. So FX equals zero, Y equals six. So it cannot be me. Now we look at as choice a negative 12. So if we see that we have a line angled downwards and it intersects the Y axis at, at six, at a Y six, if it intersects the Y axis at six or X equals zero, anything before the Y axis or any X before the Y axis will have a Y value greater than six because the line is angled downwards. Therefore, at an X of FX is equal to negative 12, Y will be greater than six. So once again, it won't be equal to zero and it won't be approaching zero. So we can emanate as choice A. Now we have enter choices C and D. Well, let's look at answer choice C, they're asking us that they're giving us an X value of six. We see that at six, it intersects the graph one Y equals three. So if X equals six Y is around three, and we just see that by looking at our graph and estimating, so we can also eliminate X equals six. So answer choice six C. Now we look at A D which is 12 and we look at our graph. Now we only have the graph up to X equal 10. However, we can see that our graph is angled downwards and it hasn't intersected the X axis at 10 yet. And that's what, so we know it's gonna be after 10 and it's very close to intersecting it. So just by looking at that, we can infer that at around fx equals 12, it is possible that why will be equal to zero? And that is what we're looking for. We're looking for the most likely solution. So in this case, 12 will be that most likely solution because we have a graph angle downwards that hasn't intersected the X axis at X of 10 yet, but it's very close to it. So we can confidently say that answer choice D or will be the answer to this question. So I hope that was helpful. And until next time

Solve each problem. A graph of y=ƒ(x) is shown in the standard viewing window. Which is the only value of x that could possibly be the solution of the equation ƒ(x) =0? A. -15 B. 0 C. 5 D. 15

Key Concepts

Zero of a Function

Interpreting Graphs

Linear Functions and Their Graphs

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