Identifying polynomial functions

Question

For each function, determine whether it is a polynomial function.

A. v(x) = x⁸ - 7x + 3x^-7

B. g(x) = 3√x - 9x⁵

C. h(x) = - 9/x²

D. f(x) = 7x⁷

^{is it a function or not?}

Answer 1

a function passes the vertical line test, just one value of y for one value of x

if there are two values of y for one value of x then it's not a function

h(x) = -9/x^2

use a graphing caluculator, if a vertical line goes through the graph intersecting more than once, it's not a function

odd powers are functions such as D) f(x)=7x^7

x^1, x^3,x^5, x^7, x^131, x^7005, all are functions

B) g(x) is a function, as it's the sum or difference of 2 functions

A) v(x) from the graph looks like a function, as it passes the vertical line test

C) h(x) =-9/x^2 is similarly a function

they're all functions, but not all one to one functions,

as then you need to apply the horizontal line test in addition to the vertical line test