6. f(x) = x f(x) = x f(x) = x f(x) = 3 x. 10. f(x) = x + 3

Transcription

1 Section 9.1 The Square Root Function Eercises In Eercises 1-, complete each of the following tasks. i. Set up a coordinate sstem on a sheet of graph paper. Label and scale each ais. ii. Complete the table of points for the given function. Plot each of the points on our coordinate sstem, then use them to help draw the graph of the given function. iii. Use different colored pencils to project all points onto the - and -aes to determine the domain and range. Use interval notation to describe the domain of the given function. 1. f() = f() 2. f() = f() 3. f() = f() 5. f() = f() 6. f() = f() 7. f() = f() 8. f() = f() 9. f() = f(). f() = f() 4. f() = f() 1 Coprighted material. See:

2 880 Chapter 9 Radical Functions In Eercises 11-20, perform each of the following tasks. i. Set up a coordinate sstem on a sheet of graph paper. Label and scale each ais. Remember to draw all lines with a ruler. ii. Use geometric transformations to draw the graph of the given function on our coordinate sstem without the use of a graphing calculator. Note: You ma check our solution with our calculator, but ou should be able to produce the graph without the use of our calculator. iii. Use different colored pencils to project the points on the graph of the function onto the - and -aes. Use interval notation to describe the domain and range of the function. 11. f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = To draw the graph of the function f() = 3, perform each of the following steps in sequence without the aid of a calculator. i. Set up a coordinate sstem and sketch the graph of =. Label the graph ii. Set up a second coordinate sstem and sketch the graph of =. iii. Set up a third coordinate sstem and sketch the graph of = ( 3). This is the graph of f() = 3. Use 22. To draw the graph of the function f() = 3, perform each of the following steps in sequence. i. Set up a coordinate sstem and sketch the graph of =. Label the graph ii. Set up a second coordinate sstem and sketch the graph of =. iii. Set up a third coordinate sstem and sketch the graph of = ( + 3). This is the graph of f() = 3. Use 23. To draw the graph of the function f() = 1, perform each of the following steps in sequence without the aid of a calculator. i. Set up a coordinate sstem and sketch the graph of =. Label the graph ii. Set up a second coordinate sstem and sketch the graph of =. iii. Set up a third coordinate sstem and sketch the graph of = ( + 1). This is the graph of f() = 1. Use

3 Section 9.1 The Square Root Function To draw the graph of the function f() = 1, perform each of the following steps in sequence. i. Set up a coordinate sstem and sketch the graph of =. Label the graph ii. Set up a second coordinate sstem and sketch the graph of =. iii. Set up a third coordinate sstem and sketch the graph of = ( 1). This is the graph of f() = 1. Use In Eercises 25-28, perform each of the following tasks. i. Draw the graph of the given function with our graphing calculator. Cop the image in our viewing window onto our homework paper. Label and scale each ais with min, ma, min, and ma. Label our graph Use the graph to determine the domain of the function and describe the domain with interval notation. ii. Use a purel algebraic approach to determine the domain of the given function. Use interval notation to describe our result. Does it agree with the graphical result from part (i)? In Eercises 29-40, find the domain of the given function algebraicall. 29. f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() =

4 882 Chapter 9 Radical Functions 9.1 Answers 1. Domain = [0, ), Range = (, 0] f() Domain = [0, ), Range = [2, ) f() f()= +2 f()= 3. Domain = [ 2, ), Range = [0, ) f() f()= Domain = [ 3, ), Range = [2, ) f() f()= +3+2

5 Section 9.1 The Square Root Function Domain = (, 3], Range = [0, ). 15. Domain = [ 5, ), Range = [1, ) f() f()= 3 f()= Domain = [ 4, ), Range = (, 0]. 11. Domain = [0, ), Range = [3, ). f()= +3 f()= Domain = [0, ), Range = (, 3]. 13. Domain = [2, ), Range = [0, ). f()= 2 f()= +3

6 884 Chapter 9 Radical Functions 21. Domain = (, 3], Range = [0, ). 27. Domain = (, 3] f()= 12 4 f()= Domain = (, 1], Range = [0, ). f()= [ 9 2, ), 3 8, 4 3, 2 7 [ 1 2, ), Domain = [ 7/2, ) f()=