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3 years ago

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Write a rational function with no vertical asymptotes and no holes. Please explain.

1 answer:

Ksju [112]3 years ago

4 0

ANSWER

$f(x) = \frac{ {x}^{2} }{ {x}^{2} + 1 }$

EXPLANATION

We write the function such that both the numerator and the denominator are prime.

An example of a rational function with no vertical asymptotes and no holes is

$f(x) = \frac{ {x}^{2} }{ {x}^{2} + 1 }$

For the above rational function, the denominator is never zero, so there are no vertical asymptotes.

Also the highest common factor for the numerator and the denominator is 1 so there are no holes.

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Let $f(x) = 2x^2 + 3x - 9,$ $g(x) = 5x + 11,$ and $h(x) = -3x^2 + 1.$ Find $f(x) - g(x) + h(x).$

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Given that:

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and

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Then;

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Simplify;

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QUESTION 2

Given that;

$f(x)=4x-7$ .

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and

$s(x)=f(x)+g(x)$

Substitute the functions;

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Substitute x=3

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QUESTION 3

Given:

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$f(g(x))=3x^2-15x-1$

QUESTION 4

The given function is;

$f(x)=3(x-6)^2+1$

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$y=3(x-6)^2+1$

$\Rightarrow y-1=3(x-6)^2$

$\Rightarrow \frac{y-1}{3}=(x-6)^2$

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$\Rightarrow x=6+\sqrt{\frac{y-1}{3}}$

The range is:

$\frac{y-1}{3}\ge0$

$y-1\ge0$

$y\ge1$

The interval notation is;

$[1,+\infty)$

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