Chapter 7 – Radical Equations and Inequalities 7.3 – Square Root Functions and Inequalities

 In this section we will learn how to:  Graph and analyze square root functions  Graph square root inequalities

7.3 – Square Root Functions and Inequalities  Square root function – a function that contains a square  Parent function – y = √x  The inverse of a quadratic function is a square root function only if the range is restricted to nonnegative numbers.

7.3 – Square Root Functions and Inequalities

 In order for a square root to be a real number, the radicand cannot be negative.  When graphing square root function, determine when the radicand would be negative and exclude those values from the domain  Just like we did when we had x values in the denominator.

7.3 – Square Root Functions and Inequalities  Example 1  Graph y = √(3/2x – 1). State the domain, range, x- and y-intercepts.

7.3 – Square Root Functions and Inequalities  Example 2  When an object is spinning in a circular path of radius 2 meters with velocity v, in meters per second, the centripetal acceleration a, in meters per second squared, is directed toward the center of the circle. The velocity v and acceleration a of the object are related by the function v = √2a.  Graph the function. State the domain and range.  What would be the centripetal acceleration of an object spinning along the circular path with a velocity of 4 meters per second?

7.3 – Square Root Functions and Inequalities  Square root inequality – an inequality involving square roots.

7.3 – Square Root Functions and Inequalities  Example 3  Graph y > √(3x + 5)

7.3 – Square Root Functions and Inequalities HOMEWORK Page 400 #9 – 19 odd, 21 – 23 all, 25 – 29 odd