Respuesta :

benmartin

Hi! I'd be happy to help you. However, there is not enough information here for us to help, as there is no way to tell which graph is correct without the equations of f(x) and g(x). They'd look something like:

"f(x) = x-2," or "g(x) = 7x+3."

Are you able to provide the equations of of f(x) and g(x)? I would be more than happy to help.

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UPDATE: I did not realize that you could solve this problem without the original equations. Please refer to the other user's response for an amazing and detailed explanation of this problem! :)

xKelvin

Answer:

The first graph.

Step-by-step explanation:

We want to find the graph that shows:

[tex]h(x)=f(x)g(x)[/tex]

Notice that g(x) is a line and f(x) is a quadratic.

So, their product must be a cubic.

Also, g(x) and f(x) is the same across all four graphs. The only difference is h(x).

Notice that our quadratic f(x) is curving upwards. Therefore, the leading coefficient of f(x) is positive.

Notice that the line g(x) is sloping downwards. Therefore, the leading coefficient of g(x) is negative.

So, this means that the leading coefficient of our cubic h(x) must be negative since a positive times a negative yields a negative.

Remember that the parent cubic function has a positive leading coefficient and it rises from left to right.

So, if our leading coefficient is negative, the cubic will fall from left to right.

Therefore, we can eliminate the 2nd and 3rd graphs since in those two, h(x) has a positive leading coefficient.

Now, we can just pick a test point and determine whether our graph is the first or the fourth.

Let's let x = -2. So, we have the equation:

[tex]h(x)=f(x)g(x)[/tex]

Substitute all Xs for -2s:

[tex]h(-2)=f(-2)g(-2)[/tex]

Looking at the graphs, we can see that f(-2) is 8. g(-2) is 0.5. Substituting this back, we get:

[tex]h(-2)=8(.5)=4[/tex]

So, h(-2) should be 4.

For the first graph, h(-2) is indeed 4.

For the second graph, h(-2) is 6.

So, the correct graph that represents f(x)g(x) is the first graph.

And we're done!

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