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MATH 30-1Radical Functions Module Two Assignment

Module / Unit 2 - Assignment Booklet

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Math 30-1: Module 2 Lessons Assignment 2 | P a g e


Lesson 1: Radical Functions and Transformations

1. Describe the transformations of the graph of to obtain the graphs of the following functions. State the domain and range for each function.

a.

b.

2. a. Graph using transformations. Explain your process.

b. State the domain and range of the function.


3. Explain how the parameters in the function that you learned about in

Module 1 compare to the parameters you have studied in this lesson..

4. At the beginning of the lesson, the radical function was introduced, where S is the speed of the vehicle in km/h, L is the length of the skid marks in metres, and f is the coefficient of friction. The coefficient of friction for a particular road made of asphalt

pavement is 0.80. The new function would be

a. Describe the transformations required to transform the function into the

function

b. Graph the function

c. State the domain and range. What do these values mean in the context of this question?

d. Use the graph to determine the approximate speed of the vehicle if the length of the skid marks is 20 m.


LESSON 1 SUMMARY

Refer to the Key Ideas section on page 72 of your text Pre-Calculus 12.

You should have noticed that the parameters a, b, h, and k from the general form

affect the graph of the radical equation in the following ways.

Parameter Value > 0 Value < 0

aVertical stretch of graph of

by a factor of a.

Vertical stretch of graph of

by a factor of a.

Graph of reflected in x-axis.

bHorizontal stretch of graph

of by a factor of

Horizontal stretch of graph

of by a factor of

Graph of reflected in y-axis.

hGraph of is translated to the right h units.

Graph of is translated to the left h units.

k Graph of is translated up by k units.

Graph of is translated down by k units.


Lesson 2: Square Root of a Function

1. a. Sketch the graph of the function given the graph of the function y f(x).

b. State the domain and range of the function and y f(x). Explain why the domains and ranges are similar and/or different.

2. For each point on the graph of y f(x), does a corresponding point on the graph of

exist? If so, state the coordinates (rounded to two decimal places, if necessary).

a. (1, 3)

b. (3, 4)

c. (m, n)


3. For each function, identify and explain any differences in the domains and ranges of y f(x)

and .

a. f(x) x2 – 49

b. f(x) 5x2 50

4. Write a summary of your strategy for graphing the function when you are given only the graph of y f (x).


LESSON 2 SUMMARY


In this lesson you looked at the graph of when given the graph of y = f(x). You

can use the values from the function f(x) to predict the values of the function

The y-values of the points of are the square roots of the y-values of the points on the original function y = f(x).

In terms of mapping: so The invariant points occur when f(x) = 0 and f(x) = 1 because the square root of 0 is 0 and the square root of

1 is 1. The domain of are the x-values of f(x) for which f(x) is greater than or

equal to zero. The range of are the y-values in the range of f(x) for which f(x) is defined.

f(x) f(x) < 0 f(x) = 0 0 < f(x) < 1 f(x) = 1 f(x) > 1

graph

Note: Take the square root of the y-values of y = f(x), and the range must be positive.

graph undefined

and y = f(x) graphs intersect on x-axis

graph is above y = f(x) graph

graph intersects y = f(x) graph

graph is below y = f(x) graph

Some of the key lesson points are highlighted on the following graph.


Lesson 3: Solving Radical Equations Graphically1. Solve each equation graphically. Describe the function(s) you graphed, and explain how

you determined the solution from the graph.

a. b.

2. Describe the relationship between the roots of a radical equation and the x-intercepts of the graph of the corresponding radical function.

3. How can the graph of a function be used to find the solutions to an equation? Create an example to support your answer.


4. An equation used by investigators at accident scenes was introduced in Lesson 1. To determine the vehicle’s speed before the collision, investigators may use the formula

where S is the speed in kilometres per hour of the vehicle, L is the length of the skid marks in metres, and f is the coefficient of friction. The skid mark was left by the rubber tires on wet asphalt. If the speed of the vehicle was 60 km/h and the length of the skid marks was 28 m, determine the coefficient f.


LESSON 3 SUMMARY


In this lesson you explored solving radical equations graphically. The solutions, or roots, of a radical equation are equivalent to the x-intercepts of the corresponding radical function. Two graphical methods were discussed.

Using a single function:

o Rearrange the equation so that one side is equal to zero, and then graph the function. The solution is found by determining the value of the x-intercept(s).

o The solution of the equation is x ≈ 1.73.

o The solution for the equation is 1.73.

Using a system of two functions:

o Graph each side of the equation as two separate functions. The solution is determined by the value of x at the point(s) of intersection.

o The solution of the equation is x ≈ 1.73.

Radical equations that are used in various contexts, such as accelerated motion, can be solved using a graphical method.


MODULE 2 – RADICAL FUNCTIONS SUMMATIVE ASSIGNMENT

Solve the following questions found in your text book. Show full solutions and attach to this module before you hand it in.

Module Two is now complete. Once you have received your corrected work, review your instructor comments and prepare for your module two test.

Text: Pre-Calculus 12

Section 2.1: Page 73 to 77 #5a, 5d, 5f, 15

Section 2.2: Page 86 to 89 #4, 6b, 7b, 7c, 17c

Section 2.3: Page 96 to 98 #5a, 5c, 6d, 7b

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