William Anthony Granville

“ When two variables are so related that the value of the first variable depends on the value of the second variable, then the first variable is said to be a function of the second variable.
Nearly all scientific problems deal with quantities and relations of this sort, and in the experiences of everyday life we are continually meeting conditions illustrating the dependence of one quantity on another. For instance, the weight a man is able to lift depends on his strength, other things being equal. ”

“ A variable is said to vary continuously through an interval , when starts with the value and increases until it takes on the value in such a manner as to assume the value of every number between and in the order of their magnitudes. ”

“ Similarly, the distance a boy can run may be considered as depending on the time. Or, we may say that the area of a square is a function of the length of a side, and the volume of a sphere is a function of its diameter. ”