p Graph square root functions. VOCABULARY Radical expression Radical function Square root function Parent square root function

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1 . Graph Square Root Functions Goal p Graph square root functions. Your Notes VOCABULARY Radical epression Radical function Square root function Parent square root function PARENT FUNCTION FOR SQUARE ROOT FUNCTIONS The most basic square root function in the famil of all square root functions, called the, is. The graph of the parent square root function is shown. (0, 0) 2 (, ) Copright Holt McDougal. All rights reserved. Lesson. Algebra Notetaking Guide 28

2 . Graph Square Root Functions Goal p Graph square root functions. Your Notes VOCABULARY Radical epression An epression that contains a radical, such as a square root, cube root, or other root Radical function A radical function includes a radical epression with the independent variable in the radicand. Square root function A radical function that contains a square root Parent square root function Ï } PARENT FUNCTION FOR SQUARE ROOT FUNCTIONS The most basic square root function in the famil of all square root functions, called the parent square root function, is Ï }. The graph of the parent square root function is shown. (0, 0) 2 (, ) Copright Holt McDougal. All rights reserved. Lesson. Algebra Notetaking Guide 28

3 Eample Graph a function of the form a Ï } Graph the function 24 Ï } and identif its domain and range. Compare the graph with the graph of Ï }. Step Make a table. Because the square root of a negative number is, must be nonnegative. So, the domain is Step 2 Plot the points. Step Draw a through the points. From either the table or the graph, ou can see the range of the function is. Step 4 Compare the graph with the graph of Ï }. The graph of 24 Ï } is vertical (b a factor of ) and a of the graph Ï }. Eample 2 Graph a function of the form Ï } k Graph the function Ï } 2 2 and identif its domain and range. Compare the graph with the graph of Ï }. To graph the function, make a table, then plot and connect the points. The domain is The range is. The graph of Ï } 2 2 is a (of units ) of the graph of Ï }. 282 Lesson. Algebra Notetaking Guide Copright Holt McDougal. All rights reserved.

4 Eample Graph a function of the form a Ï } Graph the function 24 Ï } and identif its domain and range. Compare the graph with the graph of Ï }. Step Make a table. Because the square root of a negative number is undefined, must be nonnegative. So, the domain is Step 2 Plot the points. Step Draw a smooth curve through the points. From either the table or the graph, ou can see the range of the function is 0. Step 4 Compare the graph with the graph of Ï }. The graph of 24 Ï } is vertical stretch (b a factor of 4 ) and a reflection in the -ais of the graph Ï }. Eample 2 Graph a function of the form Ï } k Graph the function Ï } 2 2 and identif its domain and range. Compare the graph with the graph of Ï }. To graph the function, make a table, then plot and connect the points. The domain is The range is 22. The graph of Ï } 2 2 is a vertical translation (of 2 units down ) of the graph of Ï }. 282 Lesson. Algebra Notetaking Guide Copright Holt McDougal. All rights reserved.

5 Checkpoint Graph the function and identif its domain and range. Compare the graph with the graph of Ï } Ï } Ï } Eample Graph a function of the form Ï } 2 h Graph the function Ï } and identif its domain and range. Compare the graph with the graph of Ï }. To graph the function, make a table, then plot and connect the points. To find the domain, find the values of for which the radicand,, is. The domain is The range is. The graph of Ï } is a (of units to the ) of the graph of Ï }. Copright Holt McDougal. All rights reserved. Lesson. Algebra Notetaking Guide 28

6 Checkpoint Graph the function and identif its domain and range. Compare the graph with the graph of Ï } Ï } Domain: 0; Range: 0 The graph is a vertical shrink (b a factor of 0.2) of the graph Ï } Ï } 4 Domain: 0; Range: 4 The graph is a vertical translation (of 4 units up) of the graph Ï } Eample Graph a function of the form Ï } 2 h Graph the function Ï } and identif its domain and range. Compare the graph with the graph of Ï }. To graph the function, make a table, then plot and connect the points. To find the domain, find the values of for which the radicand,, is nonnegative. The domain is The range is 0. The graph of Ï } is a horizontal translation (of units to the left ) of the graph of Ï }. Copright Holt McDougal. All rights reserved. Lesson. Algebra Notetaking Guide 28

7 GRAPHS OF SQUARE ROOT FUNCTIONS To graph a function of the form a Ï } 2 h k, ou can follow these steps. Step Sketch the graph of a Ï }. The graph of a Ï } starts at the and passes through the point. Step 2 Shift the graph h units (to the right if h is and to the left if h is ) and k units ( if k is positive and if k is negative). Eample 4 Graph a function of the form a Ï } 2 h k Graph the function Ï } 2 2. Step Sketch the graph of Ï }. Step 2 Shift the graph h units horizontall and k units verticall. Notice that h and k. Shift the graph and. 7 7 Checkpoint Complete the following eercises.. Graph the function Ï } 2 and identif its domain and range. Compare the graph with the graph of Ï }. 7 Homework 4. Identif the domain and range of the function in Eample Lesson. Algebra Notetaking Guide Copright Holt McDougal. All rights reserved.

8 GRAPHS OF SQUARE ROOT FUNCTIONS To graph a function of the form a Ï } 2 h k, ou can follow these steps. Step Sketch the graph of a Ï }. The graph of a Ï } starts at the origin and passes through the point (, a). Step 2 Shift the graph h units horizontall (to the right if h is positive and to the left if h is negative ) and k units verticall ( up if k is positive and down if k is negative). Eample 4 Graph a function of the form a Ï } 2 h k Graph the function Ï } 2 2. Step Sketch the graph of Ï }. Step 2 Shift the graph h units horizontall and k units verticall. Notice that h and k 2. Shift the graph right unit and up 2 units (, 2) (0, 0) 7 Homework Checkpoint Complete the following eercises.. Graph the function Ï } 2 and identif its domain and range. Compare the graph with the graph of Ï }. Domain: ; Range: 0; The graph of Ï } 2 is a horizontal translation (of units to the right) of the graph of Ï } Identif the domain and range of the function in Eample 4. Domain: ; Range: Lesson. Algebra Notetaking Guide Copright Holt McDougal. All rights reserved.