Let p=(x,y) be a point on the graph of y= 1/x. express the distanced from p to the point x (2,0) as a function of x. what is d if x=2?

D = SQRT (x^4 + 17x^2 + 64)    This is the distance as a function of x

Step-by-step explanation:

This problem uses the Pythagorean Theorem to determine the length of a hypotenuse of a right triangle.

The base of the triangle goes x distance along the x-axis, then y distance up to the point in question.  What is the distance (the hypotenuse of that triangle) as a function of x?

D = SQRT (x^2 + y^2)

D = SQRT (x^2 + (x^2+8)^2)         (substitute for y)

D = SQRT (x^2 + x^4 + 16x^2 + 64)        (expand using FOIL)

D = SQRT (x^4 + 17x^2 + 64)                (revise order, collect terms)

   This is the distance as a function of x