Graphing a Radical Function

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Presentation transcript:

Graphing a Radical Function www.assignmentpoint.com

Graph The domain is x > -2. The range is y > 0. www.assignmentpoint.com

Solving a Radical Equation Graphically The solution will be the intersection of the graph Solve and the graph of y = 0. The solution is x = 12. Check: L.S. R.S. www.assignmentpoint.com

Solving a Radical Equation Graphically Solve The solution is x = 3 or x = 7. www.assignmentpoint.com

Solving Radical Inequalities Solve Find the values for which the graph of Note the radical 7x - 3 is defined only when . is above the graph of y = 3. The graphs intersect at x = 4. x > 4 Therefore, the solution is x > 4. www.assignmentpoint.com

Solving Radical Equations Solve x ≥ -2 Set up the equation so that there will be one radical on each side of the equal sign. Square both sides. 2x + 4 = x + 7 x = 3 Simplify. L.S. R.S. Verify your solution. Therefore, the solution is x = 3. www.assignmentpoint.com

Squaring a Binomial (a + 2)2 = a2 + 4a + 4 ( 5 + √x - 2 )2 (a√x + b)2 Note that the middle term is twice the product of the two terms of the binomial. (a + 2)2 = a2 + 4a + 4 ( 5 + √x - 2 )2 The middle term will be twice the product of the two terms. A final concept that you should know: (a√x + b)2 = a2(x + b) = a2x + ab www.assignmentpoint.com

Solving Radical Equations Set up the equation so that there will be only one radical on each side of the equal sign. Solve Square both sides of the equation. Use Foil. Simplify. Simplify by dividing by a common factor of 2. Square both sides of the equation. www.assignmentpoint.com Use Foil.

x - 3 = 0 or x - 7 = 0 x = 3 or x = 7 Solving Radical Equations Distribute the 4. Simplify. Factor the quadratic. Solve for x. x - 3 = 0 or x - 7 = 0 x = 3 or x = 7 Verify both solutions. L.S. R.S. L.S. R.S. www.assignmentpoint.com

Solving Radical Inequalities Solve x > -1 The graphs intersect at the point where x = 8. x ≥ -1 and x < 8 The solution is -1 < x and x < 8. www.assignmentpoint.com