Find the value of x 2 + 4x + 4 if x = –2. B. 0 C. 4 D. 16 5–Minute Check 1

Evaluate |x – 2y| – |2x – y| – xy if x = –2 and y = 7. B. 9 C. 19 D. 41 5–Minute Check 3

Factor 8xy 2 – 4xy. A. 2x(4xy 2 – y) B. 4xy(2y – 1) C. 4xy(y 2 – 1) D. 4y 2(2x – 1) 5–Minute Check 4

A. B. C. D. 5–Minute Check 5

1.1 Functions Splash Screen

Objectives Use Set Notation Use Interval Notation

Set – a collection of objects Example: Colors, Cars Element – are the objects that belong to a set. Example: red, orange, blue, …. Nissan, Audi, Jeep, …

Infinite Set A set that has an unending list of elements Countable – a collection of objects Uncountable – are the objects that belong to a set.

Key Concept 1

A. Describe {2, 3, 4, 5, 6, 7} using set-builder notation. Use Set-Builder Notation A. Describe {2, 3, 4, 5, 6, 7} using set-builder notation. The set includes natural numbers greater than or equal to 2 and less than or equal to 7. This is read as the set of all x such that 2 is less than or equal to x and x is less than or equal to 7 and x is an element of the set of natural numbers. Example 1

B. Describe x > –17 using set-builder notation. Use Set-Builder Notation B. Describe x > –17 using set-builder notation. The set includes all real numbers greater than –17. Example 1

C. Describe all multiples of seven using set-builder notation. Use Set-Builder Notation C. Describe all multiples of seven using set-builder notation. The set includes all integers that are multiples of 7. Example 1

Describe {6, 7, 8, 9, 10, …} using set-builder notation. Example 1

Interval Notation Is a method of writing numbers in a set Interval Notation Is a method of writing numbers in a set. Recall the Number Line

 

A. Write –2 ≤ x ≤ 12 using interval notation. Use Interval Notation A. Write –2 ≤ x ≤ 12 using interval notation. The set includes all real numbers greater than or equal to –2 and less than or equal to 12. Answer: [–2, 12] Example 2

B. Write x > –4 using interval notation. Use Interval Notation B. Write x > –4 using interval notation. The set includes all real numbers greater than –4. Answer: (–4, ) Example 2

C. Write x < 3 or x ≥ 54 using interval notation. Use Interval Notation C. Write x < 3 or x ≥ 54 using interval notation. The set includes all real numbers less than 3 and all real numbers greater than or equal to 54. Answer: Example 2

Write x > 5 or x < –1 using interval notation. B. C. (–1, 5) D. Example 2

 

Review Homework

1.1 Functions Continued What is a function? How do we use the Vertical Line Test?

x represents the domain y represents the range Key Concept 3

Turn your pencil vertically. Does you pencil pass through the graph more than once? Key Concept 3a

B. Determine whether the table represents y as a function of x. Identify Relations that are Functions B. Determine whether the table represents y as a function of x. Answer: No; there is more than one y-value for an x-value. Example 3

C. Determine whether the graph represents y as a function of x. Identify Relations that are Functions C. Determine whether the graph represents y as a function of x. Answer: Yes; there is exactly one y-value for each x-value. Any vertical line will intersect the graph at only one point. Therefore, the graph represents y as a function of x. Example 3

Practice WKST

Review Homework And Worksheet

Extra Help – Second half of Lunch Quiz on Section 1.1 Tuesday, September 16 Day 4 Extra Help – Second half of Lunch

1.1 – Functions Objectives Determine if the equation is a function Find function values Find the domain of the function

D. Determine whether x = 3y 2 represents y as a function of x. Identify Relations that are Functions D. Determine whether x = 3y 2 represents y as a function of x. To determine whether this equation represents y as a function of x, solve the equation for y. x = 3y 2 Original equation Divide each side by 3. Take the square root of each side. Example 3

Answer: No; there is more than one y-value for an x-value. Identify Relations that are Functions This equation does not represent y as a function of x because there will be two corresponding y-values, one positive and one negative, for any x-value greater than 0. Let x = 12. Answer: No; there is more than one y-value for an x-value. Example 3

Determine whether 12x 2 + 4y = 8 represents y as a function of x. A. Yes; there is exactly one y-value for each x-value. B. No; there is more than one y-value for an x-value. Example 3

To find f (3), replace x with 3 in f (x) = x 2 – 2x – 8. Find Function Values A. If f (x) = x 2 – 2x – 8, find f (3). To find f (3), replace x with 3 in f (x) = x 2 – 2x – 8. f (x) = x 2 – 2x – 8 Original function f (3) = 3 2 – 2(3) – 8 Substitute 3 for x. = 9 – 6 – 8 Simplify. = –5 Subtract. Answer: –5 Example 4

B. If f (x) = x 2 – 2x – 8, find f (–3d). Find Function Values B. If f (x) = x 2 – 2x – 8, find f (–3d). To find f (–3d), replace x with –3d in f (x) = x 2 – 2x – 8. f (x) = x 2 – 2x – 8 Original function f (–3d) = (–3d)2 – 2(–3d) – 8 Substitute –3d for x. = 9d 2 + 6d – 8 Simplify. Answer: 9d 2 + 6d – 8 Example 4

C. If f (x) = x2 – 2x – 8, find f (2a – 1). Find Function Values C. If f (x) = x2 – 2x – 8, find f (2a – 1). To find f (2a – 1), replace x with 2a – 1 in f (x) = x 2 – 2x – 8. f (x) = x 2 – 2x – 8 Original function f (2a – 1) = (2a – 1)2 – 2(2a – 1) – 8 Substitute 2a – 1 for x. = 4a 2 – 4a + 1 – 4a + 2 – 8 Expand (2a – 1)2 and 2(2a – 1). = 4a 2 – 8a – 5 Simplify. Answer: 4a 2 – 8a – 5 Example 4