Functions Make a statement about functions. What do you notice about all 4 graphs?

NON-Functions Make a statement about non-functions. What do you notice about all 3 graphs?

Which one is NOT a function? Function: a relationship where each x-value has exactly one y-value Which one is NOT a function?

Vertical Line Test Non-Function Function Function If a vertical line intersects the graph more than once, the relation is NOT a function Non-Function Function Function

Notes Each x-value has exactly One y-value A x-value has more than one y-value Passes the Vertical Line Test (no vertical line intersects the graph more than once) Fails the Vertical Line Test (a vertical line intersects the graph more than once) Students should write this in their notes before the activity.

Organize Cards into columns Check your answers Activity Cut out Cards Organize Cards into columns Check your answers Glue Card in correct column Pass out cut and paste activity to be done in NOTEBOOKS

𝒚=𝟐𝒙 Equations  Functions 𝒚 = 𝒙 𝟐 𝒚 = 𝟑 𝒙 x y –3 1 27 –1 1 3 2 9 3 27 𝒚 = 𝒙 𝟐 𝒚 = 𝟑 𝒙 1. 2. 3. x y –3 1 27 –1 1 3 2 9 3 27 x y 1 2 5 10 7 14 x y –4 16 –1 1 5 25

Vocabulary Of A Function Independent Variable Dependent Variable x-values y-values Domain Range Input Output x f (x) NEW

𝒚=𝟐𝒙 Function Notation f(x) 𝒚 = 𝒙 𝟐 f(x) f(x) 𝒚 = 𝟑 𝒙 x y –3 –1 2 9 3 𝒚 = 𝒙 𝟐 f(x) f(x) f(x) 𝒚 = 𝟑 𝒙 1. 2. 3. x y –3 –1 2 9 3 27 x y 1 2 5 10 7 14 x y –4 16 –1 1 5 25

Evaluate a Function using a Graph f (x) = y 1 2 3 4 5 6 7 8 x f (2) = 4 f (3) = 5 f (7) = 4 f (2)

Evaluate a Function using Algebra f (x) = 3 x – 2 f (1) = 3(1) – 2 = 1 f (4) = 3(4) - 2 = 10 f (0) = 3(0) - 2 = -2

Classwork: Choose A, B or C 0 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 f (x) = x – 5 g(x) = 1.5x f (8) = 3 g(8) = 12 f (3) = -2 g(10) = 15 g(-.5) = f (-2)= -.75 -7 f(2) = 4 f(0) = f(7) = 1

Working Backwards If 𝑓 𝑥 =−5𝑥+7 and 𝑓 𝑥 =−168, find 𝑥. −168=−5𝑥+7 −175=−5𝑥 𝑥=35 If 𝑓 𝑥 =3 𝑥 2 +1 and 𝑓 𝑥 =49, find 𝑥. 49=3 𝑥 2 +1 48=3 𝑥 2 16= 𝑥 2 𝑥=±4

Evaluating Functions Practice Complete the problems on a separate sheet of paper. Your answer should be in the form: 𝑓 7 =−3 If you need help, ask your tablemates If 𝑓 𝑥 =𝑥+5, find 𝑓(10) If 𝑓 𝑥 =3𝑥−9, find 𝑓(−6) If 𝑓 𝑥 =3 4 𝑥 , find 𝑓(2) If 𝑓 𝑥 = 𝑥 2 +6𝑥−3, find 𝑓(2) If 𝑓 𝑥 =2 𝑥+7 −3𝑥 and 𝑓 𝑥 =13, find 𝑥 If 𝑓 𝑥 = 3𝑥 2 −11𝑥−1, and 𝑓 𝑥 =3, find 𝑥 𝑓(10)=15 𝑓 −6 =−27 𝑓(2)=48 𝑓(2)=13 𝑥=1 𝑥=4 and 𝑥=−1/3

Would You Rather…? Would you rather give up television or fast food for the rest of your life?

Exit Slip Complete the exit slip without using your notes When you’re done, turn it in on the grey table and work on your homework

Optional book practice : 1-22, 1-66, 1-87, CL-120, 2-8, 2-102 1-41, 1-52, 1-53, 1-64, 1-70, 1-77, 1-85, CL – 126, 2-15, 2-48, 2-50 If book available 1-39, 1-69, 1-94, CL-122a, 2-7, 2-25, 2-27, 2-38 1-35, 1-36, 1- 60, 1-63, 1-91, CL – 121, 2-26, 2-105

Homework