Morning Pre-Calc.! Today is all about Lines Please do the following: 1)Take an entry ticket from the side shelf. 2)Take out U1L3 Notes, a pencil, and ruler. 3)Take out HW #3. Homework: o Hw #4 pg. 24 #13-29 odd, 37, 40, Updates:Chapter 1 Test is August 26 th /27 th ( , 1.8) 1/5° Due – 8/21 6° Due – 8/22 1/5° Due – 8/21 6° Due – 8/22

Agenda 1)Entry Ticket 2)Review HW #3 3)Wrap-Up U1L2 4)Graphing Linear Equations (1.3) 5)Cool-Down

Entry Ticket #2

Review HW #3 On doc. Camera.

Composition of Functions (2) Practice: State the domain of (f g)(x) for f(x) = and g(x) = How can you check to see if your final domain is correct? Composition of Functions continued… o The domain of f g includes all of the elements x in the domain of g for which g(x) is in the domain of f. o A composition of function is called an iteration, meaning taking the output and plugging it back in.

Composition of Functions (3) Practice: Find the first three iterates, x 1, x 2, and x 3, of the function f(x) = 3x + 2 for an initial value of x 0 = 4. Knowing the definition of an iteration, how do you plan to find x 1 ? We are going to skip the cool down (you may cross it off).

Graphing Linear Equations Thinking back to the entry ticket, we had a linear equation. If I asked you to graph 3x + 4y = -3 what would you do? Discuss in your tables. Linear Equations o Are commonly written in standard form. Ax + By + C = 0 where A, B, and C are constants such that A and B are not both 0. o Are commonly written in slope-intercept form. o Only two points are needed to graph a linear equation.

Graphing Linear Equations Now, you already mentioned ways you would graph a linear equation. The methods we are going to focus on today are:  x and y intercepts  Slope-Intercept Form Please write these bullets as the titles for the boxes under “Techniques for Graphing Linear Equations” on your guided notes. Recall, how many points do you need to create a line?

Learning Objective U1L3 By the end of this period you will be able to: o Graph linear equations. o Find zeros of linear functions.

Graphing Linear Equations Intercepts o x-intercept is the point where the line crosses the x-axis. o When solving for the x-intercept substitute 0 for y. o y-intercept is the point where the line crosses the y-axis. o When solving for the y-intercept substitute 0 for x. To be an x-intercept the line crosses the x-axis, what is the y-value at this point? If I was to solve for the x-intercept how could I do this?

Graphing Linear Equations (1) Practice: Graph the linear equation using the given method. (a)x and y intercepts.4x – 5y = 10

Graphing Linear Equations Slope – Intercept Form o o Slope is the change in y-values over the change in the x-values. o o The steepness of a line.

Graphing Linear Equations (1)Practice: Graph the linear equation using the given method. (b) Slope-Intercept Form. 8x + 4y = -12

Graphing Linear Equations Take 2 minutes to complete (c) and (d) on your own.

Graphing Linear Equations Slope Formula o o The change in y-values over the change in the x-values. o The steepness of a line. (2) Practice: Use the slope formula to determine the slope of JK through J(3,1) and K(2,-1).

Graphing Linear Equations Types of Slopes Knowing the types of slopes will help you identify if your graph is in the right direction.

Graphing Linear Equations H orizontal line V ertical line O Slope U ndefined slope Y = equation (crosses the y-axis) X = equation (crosses the x- axis)

Graphing Linear Equations (3) Practice: Graph the linear equation and identify the type of slope (positive, negative, 0, or undefined). (a)f(x) = -3 (b)y = 5x + 60 (c)x = -4

Show Down! You will need your whiteboards! (Under your desks) I am going to pose a question to you all and you are going to answer the problem as quick as you can on your whiteboard. BUT, hide your answer! You are competing against the others at your table. To be the table winner you must have speed and accuracy! When I say Show Down you all will show your work and keep track of who is getting the answers correct.

Show Down!  Name the x intercept of 4x + 2y = -8  Rewrite in slope-intercept form. –x + 2y – 5 = 0  Name the y-intercept of y = -0.5x.  Graph 3x + y = 6 on your whiteboard.  Graph x = 6. What type of slope does it have? Stand up if you are the table winner. (Yes, you may have more than one per table) Lets give a round of applause!

Graphing Linear Equations Linear Functions have solutions and those solutions are called zeros (or roots). Zeros o Where the graph touches the x-axis. o Where f(x) or y is set to zero. o Yes, this is the x-intercept! What is the difference you ask? Zeroes or also known as roots, are referred to as the solution of an equation vs. the intercepts are referred to as an aid in graphing the equation. Why can’t we just use the zeros to graph a linear function?

Graphing Linear Equations (4) Practice: Determine the zeros. (a) f(x) = 1.5x +3 (b) y = x 2 – 4 (c) f(x) = 5 What is the name of the function in ©?

Graphing Linear Equations Now, there might a time when you are trying to graph an equation at home and you are doubting your abilities. You can use the graphing calculator to check your work! Graph 3x + 7y = 14 on your calculator. Discuss a plan of action with your tablemates. How will you graph this equation? Play with your calculator. Can you figure it out?

Graphing Linear Equations Steps: (1) Put into slope-intercept form. (2) Go to y= in calc and type in slope intercept form. (3) Push ZOOM then 6:Zstandard [this gives a window of -10 to 10] (4) If you do not see your graph go to WINDOW and adjust accordingly. [You want to see the intercepts.] Try to graph the following: 23y - 20x = 920

Cool Down… On your guided notes write to an absent student. Choose one concept we learned today and explain it in detail. Take 4 minutes to complete this cool-down. Then we will share aloud.

Study Tools When we finish lessons early we are going to focus on study tools. Why? From my previous experience as a teacher most students perform poorly on assessments (quizzes or tests) because they do not know how to study. I will teach you all how to prepare and to use your resources to become successful students!

Study Tools Study Tool Topic – How to use notecards effectively Write your own definitions… Do Not Copy Out of the Book Go through your deck of cards and create a pile of what you know and don’t know. When you have 7 cards that you don’t know stop and go through those 7 cards until you are comfortable with them. – Why 7? Your short-term memory can only hold 7 plus or minus an item. The more you chunk your items in 7 the easier it is for your long term memory to store it for future use. What should you write on notecards? Anything you are unsure of or do not want to forget! You can draw pictures or write words or both! These are yours so it must help you study not me. I will provide 15 cards per table. Please begin creating your notecards. If you need help in choosing items or how to write your own definitions please ask me or your tablemates.

Study Tools Switch notecards with another tablemate. Do you think anything is incorrect on your peers notecard? If so discuss with tablemates to check. If you are still unsure ask me! Peer Study!