Lesson 7.3Square Root Functions and Inequalities

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Square Root Functions

• Definition: when a function contains a square root of a variable

• The inverse of a quadratic function (starts with x2) is a square root function only if the range has no negative numbers!!

xy

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Parent Functions xy 2xy

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Graphing Square Root Functions

1. Find the domain. The radicand (the stuff inside the square root) cannot be negative so take whatever is inside and make it greater than or equal to 0 and solve.

2. Plug the x value you found back in and solve for y.

3. Make a table starting with the ordered pair you found in steps 1 & 2. Graph.

4. State the range.

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Examples1. Graph. State the domain, range, and x- and y-

intercepts.

43 xy

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2. Graph. State the domain, range, and x- and y- intercepts.

532 xy

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3. Graph. State the domain, range, and x- and y- intercepts

12

3 xy

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Square Root Inequalities

•Follow same steps as an equation to graph but add last step of shading.

•Remember rules for solid and dotted lines!!

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Examples4. Graph 62 xy

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5. Graph 1 xy

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6. Graph

153 xy

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7. Graph

422 xy