Solving Rational Equations on a Graphing Calculator

Key Questions

  • How do you solve a rational equation by using a graph?

    Answer:

    Please see below.

    Explanation:

    To solve any equation f(x)=0, we have to just draw a graph of the function in Cartesian coordinates so that y=f(x).

    Now, the value of x at points where graph of f(x) cuts x-axis gives the solution of equation f(x)=0, whatever it is trigonometric or rational.

    For example, let there be a trigonometric function f(x)=sinx, the graph shows its solution as x=npi, where n is an integer.

    graph{sinx [-10, 10, -5, 5]}

    or if the function is rational such as f(x)=x(x+0.75)(x+0.25)(x-0.5)(x-1.5)(x-2.3), solution of x(x+0.75)(x+0.25)(x-0.5)(x-1.5)(x-2.3)=0 is {-0.75,-0.25,0,0.5,1.5,2.3)

    graph{x(x+0.75)(x+0.25)(x-0.5)(x-1.5)(x-2.3) [-1.385, 3.615, -1.06, 1.44]}

    Shwetank Mauria · 1 · Jul 29 2016
  • What are you looking for when you are solving a rational equation on a graphing calculator?

    Answer:

    Usually, the intersection of the equation line with the x-axis.

    Explanation:

    What most expressions and equations are trying to find is a particular unknown value (variable) related to the other values in the expression. Numerically, we simply derive the number value from algebraic manipulations and properties. Graphically, with nominal "x" and "y" axes the usual unknown value is designated as the "x".

    So, plotting the equation on a graph will result in one of the points being ON the x-axis (or maybe it will be the ONLY point in the solution). That is the point where the value of "x" satisfies the equation.

    SCooke · 1 · Nov 27 2017

Questions

Solving Rational Equations