Question

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

Answer 1

Answer:

Equation: $f'"(x) = -\frac{1}{x-5}-7$

Asymptotes: $(x,y) = (5,-7)$

Step-by-step explanation:

Given

Let the reciprocal function be:

$f(x) = \frac{1}{x}$

First, it was reflected across the x-axis.

The rule is: (x,-y)

So, we have:

$f'(x) = -\frac{1}{x}$

Next, translated 5 units right.

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

So:

$f"(x)= -\frac{1}{x-5}$

Lastly, translated 7 units down.

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

So:

$f'"(x) = -\frac{1}{x-5}-7$

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

i.e.

$x - 5 = 0$

$x = 5$

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

i.e.

$y = -7$

$(x,y) = (5,-7)$