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nekit [7.7K]
2 years ago
5

Graph the function f(x) = x3 – 3x – 2. Based on the graph, which value for x is a double root of this function? a.–2 b.–1 c.1 d.

2

Mathematics
1 answer:
dalvyx [7]2 years ago
6 0
To solve the problem shown above you must apply the following proccedure:

 1. You have the following function given in the problem:

 <span> f(x)=x3–3x–2

 2. When you give values to the x and plot each point obtained, you obtain the graph shown in the figure attached.

 3. Based on the graph and analizing the alternate form:

 f(x)=(x-2)(x+1)</span>²

 As you can see, there is two roots x=-1, then, you can conclude that the correct answer is the option b, which is:

 b) -1
<span>
 </span>

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Write an equation for a rational function with: Vertical asymptotes at x = -3 and x = -4 x-intercepts at x = 3 and x = 4 Horizon
sattari [20]

Answer:

(10x ^ 2 - 70 * x +120) / (x ^ 2 + 7 * x +12)

Step-by-step explanation:

First a rational function is a function that is in the form a / b.

Knowing this, we proceed to calculate the asymptotes in x.

Vertical asymptotes

So that there is an asymptote in x, in a rational function the easiest thing is that the denominator is 0. Therefore, for the asymptotes x = -3 and x = -4, we make it 0 in both cases. That is to say:

x + 3 = 0

x + 4 = 0

both, in the denominator. For the moment it would be something like this:

 1 / (x + 3) * (x + 4)

X Intersections

Now, for intersections, what we should do equation 0, and that the solution of x us of the value we want, in this case x = 3 and x = 4. Because here the denominator does not influence because when equal to 0 to a rational function, the denominator becomes 0. Similarly, it is equal to 0 as in the previous case, only this time they would go in the numerator. It would be:

x - 3 = 0

x - 4 = 0

 Therefore, the function would go like this: (x - 3) * (x - 4) / (x +3) * (x + 4),

Operating the following we have:

(x ^ 2 -4 * x - 3 * x +12) / (x ^ 2 + 4 * x + 3 * x +12)

(x ^ 2 - 7 * x +12) / (x ^ 2 + 7 * x +12)

having asymptotes at x = -3 and x = -4, and intersection at (3.0) and (4.0), that is x = 3 and x = 4.

Horizontal asymptote.

Finally, in the case of the horizontal asymptote, which must be y = 10, what must be done is to divide all the terms by the highest degree term, in this case it is x ^ 2. It would be as follows:

(x ^ 2 / x ^ 2 - 7 * x / x ^ 2 + 12 / x ^ 2) / (x ^ 2 / x ^ 2 + 7 * x / x ^ 2 + 12 / x ^ 2)

Now, x ^ 2 / x ^ 2 = 1, and all the others have to be 0, therefore it would remain (1 + 0 + 0) / (1 + 0 + 0) = 1

So for the asymptote to be 10, the entire denominator must be multiplied by 10, thus being:

10 * (x ^ 2 - 7 * x +12) / (x ^ 2 + 7 * x +12)

(10x ^ 2 - 70 * x +120) / (x ^ 2 + 7 * x +12)

And this equation would already comply with everything required in the problem.

8 0
3 years ago
Quadrilateral ABCD is translated 7 units down and 2 units to the right.
disa [49]
Answer: B.) 3 units and G.) Remain the same

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2 years ago
What is the volume of the figure?
Usimov [2.4K]
The answer is C) 108 cubic units.
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What is the value of h?<br><br> h = 20<br> h = 35<br> h = 55<br> h = 70
Makovka662 [10]
The interior angles next to the 2h angles are congruent and each one measures 70 degrees. Since the interior angle is 70 degrees  the exterior angle is 110 degrees.
2h = 110
divide both sides by 2
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8 0
3 years ago
Read 2 more answers
Evalue f(x)=(-2)^2-3(-2)+5/(-2)^2+1
Nina [5.8K]
F(x)=4+6+5/4+1
F(x)=4+6+5/5
F(x)=10+1=11

Answer =11
8 0
2 years ago
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