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1 year ago

7

Why are asymptotes important in rational function graphs

1 answer:

leonid [27]1 year ago

6 0

Answer:

when sketching the curves of functions.

Step-by-step explanation:

There is a wide range of graph that contain asymptotes and that includes rational functions, hyperbolic functions, tangent curves, and more. Asymptotes are important guides when sketching the curves of functions. This is why it’s important that we know the properties, general forms, and graphs of each of these asymptotes.

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The polynomial x^2+3x-1 is a factor of x^4+3x^3-2x^2-3x+1 true or false?

pashok25 [27]

Answer:

Yes, it is true that $x^2+3x-1$ is a factor of $x^4+3x^3-2x^2-3x+1$ .

Step-by-step explanation:

Let us try to factorize $x^4+3x^3-2x^2-3x+1$

$x^4+3x^3-2x^2-3x+1\\\Rightarrow x^4-2x^2+1-3x+3x^3$

Let us try to make a whole square of the given terms:

$\Rightarrow (x^2)^2-2\times x^2 \times 1+1^2+3x^3-3x\\\Rightarrow (x^2-1)^2+3x^3-3x\\$

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Formula used above:

$a^{2} -2 \times a \times b +b^{2} = (a-b)^2$

In the above equation, we had $a = x, b = 1$ .

--------------

Further solving the above equation, taking $3x$ common out of $3x^3-3x$

$\Rightarrow (x^2-1)^2+3x(x^2-1)\\$

Taking $(x^{2} -1)$ common out of the above term:

$\Rightarrow (x^2-1)((x^2-1)+3x)\\\Rightarrow (x^2-1)(x^2+3x-1)$

So, the two factors are $(x^2-1)\ and\ (x^2+3x-1)$ .

$\therefore$ The statement that $x^2+3x-1$ is a factor of $x^4+3x^3-2x^2-3x+1$ is <em>True.</em>

7 0

3 years ago

Is order of operations and number of operations the same thing?

KonstantinChe [14]

No order of operations is what you might know as Pemdas ,number of Operations is something iv'e never heard of.

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3 years ago

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Citrus2011 [14]

Answer:

=43.98

Step-by-step explanation:

put in calculator

43.98229715

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3 years ago

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The value of n is a distance of 1.5 units from -2 on a number line . Click on the number line yo show the possible vault of n.

STatiana [176]

Answer:

I don't know

Step-by-step explanation:

I don't know

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3 years ago

Can someone help a struggling person out. I forgot how to do this.

NeX [460]

Answer:

y= -3x+3/2

Step-by-step explanation:

Write it in the form of y=mx+b because that is the y-intercept form.

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3 years ago

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