Graphs That Are Not Functions Of X. If any vertical line intersects the graph in more than one point the graph does not represent a function. Recall that if f is a polynomial function the values of x for which latex f left x right 0 latex are called zeros of f if the equation of the polynomial function can be factored we can set each factor equal to zero and solve for the zeros.
This curve fails the vertical line test. When a linear asymptote is not parallel to the x or y axis it is called an oblique asymptote or slant asymptote a function f x is asymptotic to the straight line y mx n m 0 if in the first case the line y mx n is an oblique asymptote of ƒ x when x tends to and in the second case the line y mx n is an oblique. This means that the domain which is set of x values is all real positive numbers including zero.
When a linear asymptote is not parallel to the x or y axis it is called an oblique asymptote or slant asymptote a function f x is asymptotic to the straight line y mx n m 0 if in the first case the line y mx n is an oblique asymptote of ƒ x when x tends to and in the second case the line y mx n is an oblique.
Vertical lines are not functions as the x value has infinitely many y values. The y values can be both positive and negative because y is inside absolute value symbol. If the vertical line hit the graph twice the x value would be mapped to two y values and so the graph would not represent a function. For example a student asked to graph y x 5 will correctly calculate the ordered pairs 0 5 1 4 and 2 3 and incorrectly graph a line passing through the points.
