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8/3/2019 Functions - Teacher Copy - Square Root Functions
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Square Root Functions
October 11th, 2011
Miss Connell
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This just in
We have worked with Radicals in the form of SQUAREROOTS, and those with higher root powers!
GOOD NEWS: We only have to think about the SquareRoot Function!!
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Remember Inverse?
The Inverse of a Second-Degree Polynomial Functioncorresponds to a relation defined by two square root
functions.
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The Concept
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Law of Square Roots
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Law of Square Roots
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This is rationalizing thedenominator!
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The Basic Square RootFunctionMiss Connell
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Ordered Pairs
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Visuals
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Take a few minutes to check the
parameters with your graphingcalculator:
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The TransformedSquare Root FunctionMiss Connell
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The TransformedSquare Root FunctionMiss Connell
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So.
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Critical Thinking
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Reflection about the y-axis
They set the starting point
(or end point)
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Zeros and Equations
Square Root Functions
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Steps for Finding Zeros
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Example 1
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Example 2
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Example 3
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Example 3
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Sign
To determine the sign of a square root function:
1. Draw a graph using the coordinates of the vertex and thezero, if it exists
2. Read the intervals of the domain located on either side ofthe x-axis.
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Inequalities
Square Root Function
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Graphically
1. Determine where the two curves intersect, if applicable
2. Determine the interval(s) of the domain over which theimages of the first function are greater or less than thoseof the second, based on the given inequality.
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Algebraically
1. Find an inequality in which one of the two sides consistsof a radical
2. Comparing the inequality obtained with the positiverestriction of the radical, find the inequality (orinequalities) to be solved
3. Complete the solution to the inequality (or inequalities)
4. State the Solution Set.
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Algebraic Example
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Algebraic Example
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Finding the Rule
Square Root Function
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Old Text Page 113
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Old Text Page 113
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Example
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INVERSE
The inverse of a square root function is a restrictedquadratic function
HALF OF IT!
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Properties
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Practice
Page 105 #2bdfh, 3cd, 4, 5, 6, 8, 9, 10ad,11 (graph a,c,e using your calculator, and d,b,f without)
18, 19
Page 115 #3, 4, 5, 10, 13, 14, 21, 22a, 25, 28,
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