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The reciprocal parent function is reflected across the x- axis, then translated 5 units right and 7 units down . Write an equation that could represent this new function , then identify the asymptotes

Sagot :

MrRoyalidn

Answer:

Equation: [tex]f'"(x) = -\frac{1}{x-5}-7[/tex]

Asymptotes: [tex](x,y) = (5,-7)[/tex]

Step-by-step explanation:

Given

Let the reciprocal function be:

[tex]f(x) = \frac{1}{x}[/tex]

First, it was reflected across the x-axis.

The rule is: (x,-y)

So, we have:

[tex]f'(x) = -\frac{1}{x}[/tex]

Next, translated 5 units right.

The rule is: (x,y)=>(x-5,y)

So:

[tex]f"(x)= -\frac{1}{x-5}[/tex]

Lastly, translated 7 units down.

The rule is: (x,y) => (x,y-7)

So:

[tex]f'"(x) = -\frac{1}{x-5}-7[/tex]

To get the vertical asymptote, we simply equate the denominator to 0.

i.e.

[tex]x - 5 = 0[/tex]

[tex]x = 5[/tex]

To get the horizontal asymptote, we simply equate y to the constant.

i.e.

[tex]y = -7[/tex]

[tex](x,y) = (5,-7)[/tex]

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