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Graphing a Radical Function

Learn how to graph and solve radical functions, equations, and inequalities with step-by-step instructions and examples. Master graphing, solving, and verifying solutions easily.

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Graphing a Radical Function

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  1. Graphing a Radical Function www.assignmentpoint.com

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

  3. 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. L.S. R.S. Check: 0 www.assignmentpoint.com

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

  5. 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

  6. 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

  7. Squaring a Binomial 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

  8. 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. Use Foil. www.assignmentpoint.com

  9. 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

  10. Solving Radical Inequalities x > -1 Solve 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

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