Warm Up (Nov. 30) ***Complete on handout to turn in Friday*** 1. Hana already knew 2 appetizer recipes before starting culinary school, and she will learn 2 new appetizer recipes during each week of school. After 4 weeks of culinary school, how many total appetizer recipes will Hana know? Write and solve an equation to find the answer. 2. Write a function rule XF(x)

Evaluating Functions Just plug it in and solve Function notation: f(x) The x (or variable inside the parentheses) will be replaced with a number. The x will become that number. It’s what you plug into the function to solve. So if I had f(5), x = 5 F(-60), x = -60 F(82), x = 82

Examples F(x) = x + 1 Solve and find f(43). So x = 43, then plug it in and solve = 44 So my answer is 44, or f(43) = 44 F(x) = x/4 Solve and find f(16) Answer: 4

You try F(x) = 56 – x. Solve when f(32). Answer: f(32) = 24 F(x) = 2x + 3. Solve when f(-10). Answer: f(-10) = -17

IXL practice Under Algebra 1 Q.7 Evaluate function rules I Q.12 Write a rule for a function table S.10 Linear function word problems Complete these for a grade! Ask for help if you need it.

Warm Up (Dec. 1) 1. Taylor spends $320 on groceries once a month, plus $8 per hour for a house keeper. How much should she budget for groceries and house keeping if the house keeper cleans 2 hours per week? Provide a linear function and solve. 2. Mr. Jones charges $20 plus $5.00 an hour to mow lawns. If it takes him 3 hours to mow your lawn, how much will he charge? Provide the linear function and solve. 3. Evaluate f(x) = 3(x + 12) when f(-3) 4. Write a function rule. Then fill in the rest of the table: xF(x)

Evaluating Functions: More Examples Ex 1: Evaluate f(2) for the function f(x) = x – 5 / 2x FIRST – Substitute 2 for the x value to find the value of f(x) F(2) = 2 – 5 / (2  2) THEN – Solve F(2) = -3/4 Answers to these problems can also be written as an ordered pair! (2, -3/4) Remember, ordered pairs: (x, y)

You try Evaluate f(5) for the function f(x) = 10(x – 20). Write the answer as an ordered pair. Answer: (5, -150) Remember, after you solve, that is your OUTPUT or y value. Goes in the y spot of the coordinate.

Evaluating Functions: Examples Ex 2: Evaluate the function rule f(g) = 4g + 7 to find the range for the domain {-1, 7, 9}. Let’s solve on the whiteboard. Answer: The range for the function is {3, 35, 43}

You try Evaluate the function f(p) = p for the domain {-9, - 4, 0} Plug in each input value to get your output Answer: {82, 17, 1}

Another example Given f(x) = x 3 + 4, f(5) = 113. True or false? Plug in the 5 wherever you see x in the function, then see if your output matches the output they gave you. Answer: false

Continue IXL Practice Under Algebra 1 Q.7 Evaluate function rules I (should have finished yesterday) Q.12 Write a rule for a function table S.10 Linear function word problems Q.12 and S.10 will be taken for a grade today! When you finish: p #13-20 in textbook Must finish for homework

Warm Up (Dec. 2) 1. Evaluate f(x) = 12(x 2 – 10) for the domain {-2, 5} 2. Evaluate f(x) = 4x 3 for f(2). Write your answer as an ordered pair. 3. Hannah's electricity company charges her $0.11 per kWh (kilowatt-hour) of electricity, plus a basic connection charge of $15.00 per month. Write a linear function that models her monthly electricity bill as a function of electricity usage. If Hannah uses 6 kWh of electricity, what will her bill be?

Warm Up (Dec. 3) 1. Evaluate f(x) = 5x + 3x when the domain is {−1, 1} 2. Given f(x) = 2x 2, f(11) = 242. True or false? 3. Is this a function?

Slope intercept form y = mx + b Dependent variable SlopeIndependent variable Y-intercept

Examples Identify the slope and y-intercept. y = 5x + 3 m = 5 b = 3 y = 1/2x – 1 m = ½ b = -1 (the subtraction sign makes it negative)

Slope Definition: The steepness of a line. The ratio of vertical change to the horizontal change. 4 types of slope Positive Negative Zero Undefined Rise Run “Rise over run”

Positive Slope Line that goes up from left to right

Vocabulary Increasing function– a function with a graph that goes up as it is followed from left to right An increasing function has a positive slope

Negative Slope Line that goes downhill from left to right

Vocabulary Decreasing function– a function with a graph that moves downward as it is followed from left to right A decreasing function has a negative slope

Zero Slope Lines that are horizontal have a slope of 0 m = 0

Undefined Slope Vertical lines are always undefined Rise is non-zero number, run is 0 Anything divided by 0 is undefined

How to read slope from a graph: 1. Plot two points on the line 2. Calculate rise (up or down) and run (ALWAYS run to the right) 3. Simplify if necessary Answer Slope = 2/3

Example Is the slope negative, positive, zero or undefined? If positive, run UP and to the RIGHT If negative, run DOWN and to the RIGHT Answer: m = 2

Example Is the slope negative, positive, zero or undefined? If positive, run UP and to the RIGHT If negative, run DOWN and to the RIGHT Answer: m = 3/2 = 1.5

Another example What is the slope? Answer: -3/4 Down and to the right (rise over run)

Slope Gallery Walk There are some problems posted around the room. Put your answers on notebook paper to turn in. Move freely from one station to the next (there is no particular order). No more than 3 people at a station. If you see 3 people at a station, move to one with fewer people. You may ask classmates for help getting started on a problem.

Warm Up (Dec. 2) 1. What is the slope of the line? 2. What is the y-intercept? 3. Last year, at the Marketplace Cinema, a movie ticket cost $7.50. Today (in 2013), a movie ticket can be purchased for $8.00. If theater owners predict that this pattern of increase in the cost of a movie ticket will continue, what will be the cost of a movie ticket in 2017? Model with a linear function, then solve.

Back to previous example So m = 2 What’s my y-intercept? Where does the line cross the y axis? b = -1 Put it in point slope form y = mx + b Answer: y = 2x – 1

Back to previous example So m = -3/2 = -1.5 Answer: y = -3/2x + 1

Graphing from slope-intercept form Just go backwards 1.Plot your y-intercept. Mark it with a point. 2.Then “rise and run” down/up and to the right as the slope tells you to 3.Plot multiple points, then draw a line between them. Examples: y = ½x + 4 y = 3x – 1

Warm Up Dec. 7 Find the slope from the graphs

How to write an equation in point slope form from a graph: 1. Interpret the slope of the graph and write slope in the m part of y = mx + b 2. For b (y-intercept), find the part of the line that crosses the y axis. This is where your coordinate is (0, y).

How to calculate slope from 2 points: 1.Designate which points will be x1 and x2, and which points will be y1 and y2. 2.Plug them into the formula and solve 3.Simplify if necessary

Examples Calculate the slope from given points: 1. (2, 3), (-1, 9) Answer: (10, 4), (3, 7) Answer: -3/7

Examples Calculate the slope from the given points (8, -1), (2, 10) (-2, -5), (-10, -1) (21, 11), (10, 19)

You try Calculate slope from these points 1. (4, 1), (8, 3) Answer: 1/2 2. (9, -3), (9, 8) Answer: Undefined! Anything divided by 0 is undefined, plus you can’t have repeating x’s in a function

Warm Up (Dec. 8) 1. Suppose that the function f(x) = 2x + 12 represents the cost to rent x movies a month from an internet movie club. Makayla now has $10. How many more dollars does Makayla need to rent 7 movies next month? 2. Y = -4x + 10 What is my y-intercept? What is my slope? 3. Calculate the slope from these points: (12, 4), (11, 9) 4. Calculate the slope from these points: (−9, −12), (−1, 10) 5. Y = -1/2x − 83 Identify the slope and y-intercept.

IXL Practice Grading: Must score above an 80 before you move to the next skill. I will average these scores together for your grade. Ask for help if you need it Skills: Algebra 1 S.2 Find the slope of a graph S.3 Find the slope from two points S.6 Slope-intercept form: graph an equation S.7: Write an equation from a graph

Warm Up (Dec. 9)  Calculate slope: (5, 2), (-10, 4)  Calculate slope: (0, 4), (-7, -2)  Calculate slope: (8, 4), (3, 4)  A cab company charges $1 per cab ride, plus an additional $2 per mile driven. If a cab ride is 4 miles long, how much will it cost?

Standard form Ax + By = C Coefficient Constant

How to convert from standard form to slope-intercept: Goal: Isolate the y term  Start by adding or subtracting the x term from both sides.  Then divide by the nonzero value on the y term. Example: 5x + 10y = 20 -5x 10y = 20 – 5x 10 Y = 2 – 1/2x Flip it around Y = -1/2x + 2

Example Convert from standard form to slope-intercept form: 2x + 3y = 12 Answer: -2/3x + 4 = y -10x + 5y = 20 Answer: 2x + 4 = y

You try Convert from standard form to slope intercept form 6x + 2y = 20 -3x + y = 18

Example Graph the following: 2x + 4y = 8 y = -1/2x + 2

Graph the following: Example: 3x + 5y = 15 Example: 8x – 4y = 4

Continue IXL Practice Skills: Algebra 1 S.11 Write equations in standard form S.13 Standard form: graph equation Continue working on these skills from yesterday Skills: Algebra 1 S.2 Find the slope of a graph S.3 Find the slope from two points S.6 Slope-intercept form: graph an equation S.7: Write an equation from a graph

Warm Up (Dec. 10) 1. Convert from standard form to slope intercept form: 8x – 4y = 4 2. Convert from standard form to slope intercept form: 3x + 5y = 15 Find the slope of the function or graph: 3. X = Y = 3x – 20 ***Go over what I expect on Warm Up papers

Today FIRST-- Make a list of topics on test tomorrow now There will be NO test corrections! THEN-- If you weren’t here yesterday – need to see me for notes on standard form and undefined slopes FINALLY– Make sure you have finished IXL: S.2, S.3 and S.10 AND group study

Do Now: Dec Calculate slope: (10, −3), (1,7) 2. F(x) = 3x − 8 Fill in the table. 3. Find the slope of the graph XF(x)

Do Now Dec Evaluate f(x) = 3x 2 + x + 10 when f(2). Write answer as an ordered pair. 2. Find the slope: (−5, −3), (−11, −2) 3. Change from standard form to slope intercept form: 2x + 4y = Change from standard form to slope intercept form: 6x − 3y = Fill in the table: y = −2x + 10 XY 3 −2 6

Do Now Dec Graph y = 2x Graph y = −½x using the input/output table method. Where does it cross the y axis? 3. Change 5x − 4y = 20 from standard form to slope- intercept form. 4. Change 2x − 5y = −25 from standard form to slope- intercept form.

Do Now Dec Graph y = 3/4x 2. Slope is 5 and (2,6) is on the line. Write an equation in slope intercept form. 3. Change 7x + 7y = 7 to slope intercept form and then graph.