Jennie Lai, Steven Johnson, Ayisha Stewart, & Tahira Roberts Square Root Function Jennie Lai, Steven Johnson, Ayisha Stewart, & Tahira Roberts

What is a Square Root function ? Do Now What is a Square Root function ?

Domain and Range Find the domain and range of the function y=2(√f(x)-3) Begin with what you know. You know the basic function is the sqrt(x) and you know the domain and range of the sqrt(x) are both [0,+infinity). You know this because you know those six common functions on the front cover of your text which are going to be used as building blocks for other functions.

Horizontal Shift Square Root Function √(f(x)-3) : This means that the square root function would shift horizontally to the right 3 times. Always remember that -3 means going to the right. If it is + than it would go to the left. √(f(x)-3) + 2 : For this function we can see that we are still going to shift horizontally to the right three times, but because there is a number outside of the parentheses therefore that would mean to go up 2 times.

Vertical Shift Vertical Shift- Rigid translation in that it does not change then shape or size of the graph of the function. Shift, changes the location of the graph. Vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate. Vertical and Horizontal shifts can be combined into one expression. Example  I (C) is a positive real number then the graph of f(x)+c is the graph of y=f(x) shifted upward units *If C is a positive real number the graph of f(x)-c is the graph

Shrink and Stretch When you multiply a function by a number less than 1 it shrinks, however when you multiply it by a number greater than 1 it stretches. When a graph is stretched or shrinked vertically, the x intercept does not change.

Vertical Stretch Graph the function F(x)= 2√x Find perfect squares to fit the equation. Plot the basic square root. X Y 1 4 2 9 3 16 Vertically Stretch by a factor of 2

Class work = √x Complete & Graph the Table Fraction X Y ½ 1 4 9 16

Stretch Solve and graph the following equations: 3 √x 2 √x 4 √x Remember always start with the general (perfect squares)