7-9: Square Root Functions and Inequalities

What You Will Learn  Graph and analyze square root functions.  Graph square root inequalities

Terms to Know  Square root function: a function that contains a square root of a variable. –In order for a square root to be a real number, the radicand cannot be negative. is not a function is a function Can’t be a function because of the +

Graph of square root function

Square Root Inequalities  A square root inequality is an inequality involving square roots.  You graph them exactly like a square root function, except you have to select a point and test if its ordered pair. If it is true, then shade the region with the ordered pair. If not, shade the opposite region

Graph a Square Root Function Graph. State the domain, range, x- and y-intercepts. Since the radicand cannot be negative, identify the domain. 3x + 4 > 0 x > Write the expression inside the radicand as > 0 Solve for x The x-intercept is Make a table of values and graph the function. from the graph, you can see that the domain is x>, and the range is y > 0. The y-intercept is xy

Some Practice Problems State the domain and range of each function Next slide

1. Domain: 1. Domain: x > 0 Range: 0 Range: y < 0 2. Domain: x > 0 Range: Range: y > 0 3. Domain: x 3. Domain: x > 7 Range: y > 0 Range: y > 0 4. Domain: x > 0.6 Range: y > 0 Range: y > 0