A partially completed table for the curve is given below

MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions

Problem

A partially completed table for the curve

y=\dfrac{1}{x}

is given below. Complete the table and answer the questions that follow. (a) |

x

-\tfrac34

-\tfrac12

-1

\phantom{-}\tfrac25

\phantom{-}0.8

\phantom{-}2

| |-----|-------------|--------------|-------|-------------------------|-------------------|---------------| |

y

\phantom{-}\ ?

\ ?

\ ?

\ ?

\ ?

\ ?

| Fill in each blank with the correct value of

y

in fractional form. (b) (ii) Two values of

y

are known to be

-\dfrac54

and

0.125

for the same curve. Determine the corresponding values of

x

, and insert these in an extended table column. (c) (iii) Rewrite every

y

–value in the completed table correct to three decimal places.