x and y Intercepts Of Graphs

How to find the x and the y intercepts of graphs of functionsand equations?



The x and y intercepts of a graph are points of intersection of the graph with the x axis and the y axis respectively. This a tutorial with examples and detailed solutions on how to find these points.

Example 1: Find the x and the y intercepts of the graph of function f defined by

f(x) = - 3 x + 9

Solution to Example 1

  • Since a point on the y axis has x coordinate equal to zero, to find the y interecpt, we set x to zero and find the y coordinate which is f(0).

    f(0) = -3(0) + 9 = 9

  • A point on the x axis has y coordinate equal to 0, to find the x intercept, we set y = f(x) = 0 and solve for x

    f(x) = -3 x + 9 = 0

  • Solve for x.

    x = 3

  • The x and y intercepts of the graph of f are

    x intercept: (3 , 0)

    y intercept: (0 , 9)

Example 2: Find the x and the y intercepts of the graph of the 2 variable equation given by

(x - 1) 2 + (y - 2) 2 = 16

Solution to Example 2

  • We first set x = 0 to find the y intrecpt.

    (0 - 1) 2 + (y - 2) 2 = 16

  • Solve for y

    1 + (y - 2) 2 = 16

    (y - 2) 2 = 15

    y = 2 + sqrt(15) and y = 2 - sqrt(15)

  • Set y = 0 and solve for x

    x = 1 + sqrt(12) and x = 1 - sqrt(12)

  • The x and y intercepts of the graph of the given equation are

    x intercepts: (1 + sqrt(12) , 0) and ((1 - sqrt(12) , 0)

    y intercepts: (0 , 2 + sqrt(15)) and (0 , 2 - sqrt(15))

  • The graph shown below is that of the given equation. Examine the x and y intercepts and compare to those calculated. Note that the x and y intercepts may be determined graphically.

    graph of given equation example 2


Step by Step Calculator to Find Domain of a Function New ! Free Trigonometry Questions with Answers Interactive HTML5 Math Web Apps for Mobile LearningNew !
Free Online Graph Plotter for All Devices
Home Page -- HTML5 Math Applets for Mobile Learning -- Math Formulas for Mobile Learning -- Algebra Questions -- Math Worksheets -- Free Compass Math tests Practice
Free Practice for SAT, ACT Math tests -- GRE practice -- GMAT practice Precalculus Tutorials -- Precalculus Questions and Problems -- Precalculus Applets -- Equations, Systems and Inequalities -- Online Calculators -- Graphing -- Trigonometry -- Trigonometry Worsheets -- Geometry Tutorials -- Geometry Calculators -- Geometry Worksheets -- Calculus Tutorials -- Calculus Questions -- Calculus Worksheets -- Applied Math -- Antennas -- Math Software -- Elementary Statistics High School Math -- Middle School Math -- Primary Math
Math Videos From Analyzemath
Author - e-mail


Updated: 2 April 2013

Copyright © 2003 - 2014 - All rights reserved