Radical Function

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ALBerTA DISTANCe LeArNING CeNTre MAT3791

Math 30-1 Unit 1: Functions

Lesson A: radical Functions

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Summary

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your Marks

Practice Self- Assessment 20%

Assignment 80%

Blended Booklet Grade

Alberta Distance Learning Centre 99

Mathematics 30-1: Unit 1 Lesson A - Assignment Booklet

Back to Baker Street… Complete the Back to Baker Street assignment. Refer to the Tips from Scotland Yard located at the back of this lesson booklet to assist you in completing the assignment.

Call or e-mail your teacher if you would like additional help.

Multiple-Choice Items

_________ 1. Select the best description of a radical function:

A. a function that involves a radical or root with the variable is in the index

B. a function that involves a radical or root and a variable in the radicand or under the root sign

C. a function that involves a root sign and the value under the root sign that always has the restriction that it must be greater than zero

D. a function that has a root sign in it

_________ 2. The population of grasshoppers in a certain area, in thousands, will increase according to the following function.

( )G x x3 2 1 15= - + What is the range?

A. y 15$

B. y 15#

C. x 2 1

D. x 2 1

_________ 3. The domain and range of the function f(x) = –2 ( )3x - are

A. x $ 3 and f(x) # 0

B. x $ 3 and f(x) $ 0

C x # 3 and f(x) # 0

D. x # 3 and f(x) $ 0

100 Alberta Distance Learning Centre

Lesson A - Assignment Booklet Mathematics 30-1: Unit 1

Numeric Response 1

The y-coordinate of the “endpoint” of the graph of y x4 2 3= - +^ h is

_________ 4. If f(x) = –2x2 + 18, then the range of ( )y f x4= ^ h is

A. 0 ≤ y ≤ 12 2

B. y ≤ 12 2

C. 0 ≤ y ≤ 12

D. y ≤ 12

_________ 5. The solution to the radical equation ( ) ( )x x1 5- = - may be determined by finding

A. the x-coordinate of the point of intersection of the graphs of ( )y x 1= - and ( )y x5= -

B. the x-intercept of ( ) ( )y x x1 5= - + -

C. the y-coordinate of the point of intersection of the graphs of ( )y x 1= - and ( )y x5= -

D. the y-intercept of ( ) ( )y x x1 5= - + -

Numeric Response 2

Given f(x) = 2x2 – 6 , then, to the nearest hundredth, the positive x-value that gives the smallest value of y xf= ^ h is

_________ 6. Select the interval for which y = x 252 - is undefined.

A. x > 5, x < -5

B. –5 < x < 5

C. x > 5

D. x < -5

Alberta Distance Learning Centre 101

Mathematics 30-1: Unit 1 Lesson A - Assignment Booklet

_________ 7. Determine the solution(s) of x8 13 16 9= - - and indicate the restrictions on the equation .

A. ,x x1 9 16 $= -

B. ,x x1 9 16 $= -

C. ,x x1 9 16 #= -

D. ,x x1 9 16 #=-

Numeric Response 3

When solving the radical equation x x8 6= - - , the “extraneous” root is

Use the following information to answer multiple-choice questions 8 and 9.

The time, t in seconds, it takes a pendulum to complete one back and forth swing can be determined by the equation 0.32t l= where l is the length of the pendulum in inches.

_________ 8. Determine the length of the pendulum if it takes 1.1 seconds to make a complete back and forth swing.

A. 11. 82 inches B. 10.8 inches C 9.12 inches D. 10.82 inches

_________ 9. A clock manufacturer has an adjustable length pendulum with the shortest length pendulum being 7 inches and the longest length pendulum being 11.5 inches. Determine the range of the function in this particular case.

A. 0.847 ≤ t ≤ 1.085 B. 0.847 ≤ t ≤ 0.966 C 0.966 ≤ t ≤ 1.085 D. 0.32 ≤ t ≤ 1.085

102 Alberta Distance Learning Centre

Lesson A - Assignment Booklet Mathematics 30-1: Unit 1

Written Response

1. If y = f(x) and f(x) = 2x + 5, then the graph of y = f(x) and ( )y f x= will have two common points. One common point is the x-intercept. Determine the other common point.

2. a. Express the side length of a square as a function of its area.

b. Construct a table of values and a graph to illustrate the relationship.

Alberta Distance Learning Centre 103

Mathematics 30-1: Unit 1 Lesson A - Assignment Booklet

3. Compare the domains of the functions ( )f x x= and ( )g x x2 3 5= + - . Which value in the function g(x) affected the domain of f(x)?

4. a. Graph the function f(x) = 4x2, x ≥ 0 and its inverse. Show all work and state any restrictions.

b. Determine the inverse of the function ( )f x x 2 1= . State any restrictions

and explain.

c. Explain how the answers to parts a) and b) are related.

__________________________________________________________________

104 Alberta Distance Learning Centre

Lesson A - Assignment Booklet Mathematics 30-1: Unit 1

5. a. Sketch the graphs of y = f(x) and ( )y f x= where f(x) = –3x + 6.

b. State any invariant points.

c. Explain how mapping from a linear function can assist in graphing the square root of that linear function.

__________________________________________________________________

Alberta Distance Learning Centre 105

Mathematics 30-1: Unit 1 Lesson A - Assignment Booklet

6. A roof truss is designed such that the vertical measurement from inside beam to inside beam is 2 ft 6 in.

2 ft 6 in

Determine a function for the horizontal measurement (d) of the truss.

Total: 53

106 Alberta Distance Learning Centre

Lesson A - Assignment Booklet Mathematics 30-1: Unit 1

S Standard of Excellence • Students need to make connections to other courses to complete. • Successful completion shows an ability to think beyond given examples.

Over the acceptable level of understanding • Students need to make connections from within the course notes and

example to complete. • Successful completion shows an ability to draw from given instruction and

apply skills to new problems.

L Level of acceptable standards • Students need to show an acceptable level of understanding to complete. • Successful completion shows an ability follow given examples.

V Below level of acceptable standards • Student's response to question is below acceptable standard.

E Inadequate level of acceptable standards • Student's response to question indicates student needs assistance in

understanding basic concepts.