Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Graphs of Functions(Section 1-3)

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Graph of a function f: the collection of ordered pairs (x, f(x)) such that x is in the domain of f.

If you are asked to find f(x) for a specific x value…

·If you have an equation, plug the number inside the parenthesis into the equation in place of x. The answer is the value you get once you have evaluated the expression.

·If you have a graph, look for the point on the graph where the number inside the parenthesis is the x-coordinate. The answer is the y-coordinate at this point.

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use the graph of the function to find the domain and range of f. Then find f(0).

Example 1

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use the graph of the function to find the domain and range of f. Then find f(0).

Example 2

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use the graph of the function to find the domain and range of f. Then find f(0).

Example 3

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

To determine the domain and range algebraically:·In general, the domain, is all real numbers except if there is a number that you cannot plug into the function. (ex: a number that will result in a negative number inside an even root, or that will result in a zero in the denominator of a rational expression)

·For the range, consider which y-values you can get by plugging in allowed x-values to the equation (range is easiest to determine graphically).

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use a graphing utility to graph the function and estimate its domain and range. Then find the domain and range algebraically.

Example 4 1)( 2 xxf

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use a graphing utility to graph the function and estimate its domain and range. Then find the domain and range algebraically.

Example 5 3)( tth

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use a graphing utility to graph the function and estimate its domain and range. Then find the domain and range algebraically.

Example 6 54

1)( xxf

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use the given function to answer the questions.

Example 7 f(x) = x3 – 4x

(a) Determine the domain of the function

(b) Find the value(s) of x such that f(x) = 0.

(c) The values of x from part (b) are referred to as what graphically?

(d) Find f(0), if possible.

(e) The value from part (d) is referred to as what graphically?

(f) What is the value of f at x = 1? What are the coordinates of the point?

(g) What is the value of f at x = -1? What are the coordinates of the point?

(h) The coordinates of the point on the graph of f at which x = -3, can be labeled (-3, f(-3)) or (-3, _____).

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use the given function to answer the questions.

Example 8

(a) Determine the domain of the function

(b) Find the value(s) of x such that f(x) = 0.

(c) The values of x from part (b) are referred to as what graphically?

(d) Find f(0), if possible.

(e) The value from part (d) is referred to as what graphically?

(f) What is the value of f at x = 1? What are the coordinates of the point?

(g) What is the value of f at x = -1? What are the coordinates of the point?

(h) The coordinates of the point on the graph of f at which x = -3, can be labeled (-3, f(-3)) or (-3, _____).

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Vertical line test (pg 31): A set of points in a coordinate plane is the graph of y as a function of x if and only if no vertical line intersects the graph at more than one point.

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use the Vertical Line Test to determine whether y is a function of x. Describe how you can use the graphing utility to produce the given graph.

Example 9 2

4

1xy

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use the Vertical Line Test to determine whether y is a function of x. Describe how you can use the graphing utility to produce the given graph.

Example 10 12 yx

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Increasing: positive slope

Decreasing: negative slope

Constant: zero slope

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Determine the open intervals on which the function is increasing, decreasing or constant.

Example 11

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

(A) Use a graphing utility to graph the function. (b) Determine the open intervals on which the function is increasing, decreasing or constant.

Example 12 y = x3

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

(A) Use a graphing utility to graph the function. (b) Determine the open intervals on which the function is increasing, decreasing or constant.

Example 13 y = x3 – 3x

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Section 1.3,Definitions of Relative Minimum and Relative Maximum

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use a graphing utility to approximate any relative minimum or relative maximum values of the function.

Example 14 f(x) = 3x2 – 4x – 2

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use a graphing utility to approximate any relative minimum or relative maximum values of the function.

Example 15 f(x) = -x3 + x

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

HW #61 pg 38-39 (1-41 odd…37-41 only part b)

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Test for Even and Odd Functions

A function is even if, for each x in the domain of f, f(-x) = f(x).

A function is odd if, for each x in the domain of f, f(-x) = -f(x).

**Note: Unlike a number, a function does not have to be even or odd.**

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Algebraically determine whether the function is even, odd, or neither.

Example 16 f(x) = |x|

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Algebraically determine whether the function is even, odd, or neither.

Example 17 h(x) = x3 - 5

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use a graphing utility to determine whether the function is even, odd, or neither.

Example 18 9)( xf

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

Use a graphing utility to determine whether the function is even, odd, or neither.

Example 19 3 1)( ttg

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd?

Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd.

HW #62 pg 39-41 (31-49 odd, 59-65 odd, 73-85 odd, 95-100 all)