section 2.2 square root of a...

Section 2.2 Square Root of a Function­soln.notebook

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Section 2.2 Square Root of a Function

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Examples:

1. Given , graph y = f(x) and

Method 1: Use a table of values

(Hint: You could graph y = f (x) on your graphing calculator and then use the table function to complete the second column of the table.)

a) From your table of values, determine the points of intersection.

b) Why are these points of intersection referred to as invariant points?

c) For which values of x is the graph of above the graph of ? y = f (x)

d) How are these values related to the invariant points?

e) Why is the graph of above between these points?

f) For which values of x is the graph of , below the graph of ? y = f(x)

g) Why is the graph of undefined when x > 1.5?

h) Determine the domain and range of algebraically.

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Method 2: Use Invariant Points

Steps: 1. Determine the invariant points.

2. Draw the portion of each graph between the invariant points for values of y = f (x) and that are positive but less than

3. Sketch a smooth curve above those of y = f (x) and y = g(x) in these intervals.

4. Locate other key points on y = f (x) where the values are greater than 1. Transform these points to locate image points on the graph of

5. Sketch smooth curves between the image points; they will be below those of y = f (x) in the remaining intervals. (Why??)

Section 2.2 Square Root of a Function­soln.notebook

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Key Ideas

Section 2.2 Square Root of a Function­soln.notebook

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2. Using the graph of f(x), sketch the graph of Label the invariant points and determine the domain and range of

Invariant Points

Domain

Range

Page 87, Q 1, 2, 4, 5a, c, 8a, b.

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Summary:

Lines: y = mx + b

Graph a line: 1. Plot y –intercept and use the slope or2. Find x­intercept (Set y = 0 and solve for x).

Find y­intercept (Set x = 0 and solve for y). Join the two points.

3. Create a table of values

Line with m > 0: Line with m < 0

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3. Given graph y = f(x) and (i.e )

A) Graph y = f(x).

Vertex:

y­intercept:

x­intercepts

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B) Graph

C) What are the invariant points? – Remember invariant points occur when f(x) = 0 or when f(x) = 1. i.e. Invariant points have the form (x, 1)

and (x, 0)

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D) Why is the graph of undefined ?

E) Where is the graph of above y = f(x)? below f(x)?

F) What is the domain and range of ?

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