Understanding Function Notation Video Part I Using Function

Understanding Function Notation - Video Part I Using Function Notation Part I: Understanding Function Notation

Brought to you by… MRS TUTT the most interesting teacher in the world. As a toddler she taught others to walk. She can keep one eye on the past while looking into the future.

Function Notation TONIGHT’S TARGET (Part I): I can connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1. : Y R A L U AB n o i t a t o N d r n a o d i t n a a t t o S N q on i t c n u F q put n I q ut p t u q O VOC

Relationships Spring Rainfall & Wildflowers d n e p e d s r. e l l w a f o n fl i a d l r i g W n i r p on s

Is a function of. . . Wildflowers depend on spring rainfall. Wildflowers are a function of the amount of spring rainfall. Function Notation: W(r)

Relationships Wild Rabbits & Available Food Supply d n e p e d s d t i o b f a e l R b d l a i l ai W v a e. h y t l p n o sup

Is a function of. . . Wild Rabbits depend on the available food supply. Wild rabbits are a function of the amount of available food supply. Function Notation: R(f)

Relationships Predators & The Number of Rabbits s t i b b a r f r o e r b e b m u m n u e n h e t h n T. o s r d o n t e a p d e e r d of p

Is a function of. . . The number of rabbits depend on the number of predators. The number of rabbits is a function of the number of predators. Function Notation: R(p)

Your turn! Write the following in function notation. a. Weight (W) depends on calories (c). W(c) b. Temperature (T) depends on time of day (t). c. Area (A) depends on diameter (d). T(t) A(d) d. The electric bill (B) is a function of kilowatt hours (k). B(k)

Your turn! Write a sentence giving the relationship between the two variables using “is a function of”. a. R(r) where r = amount of rainfall and R = river level. The river level is a function of the rainfall. b. P(s), where s = length of a side of a square and P = perimeter of a square. The perimeter of a square is a function of the length of the sides. c. D(n), where n = number of lawns mowed and D = dollars earned. The dollars earned is a function of the number of lawns mowed. d. M(n), where M = money spent and n = number of cd’s bought. . The money spent is a function of the number of cd’s bought.

Using Function Notation to Solve Expressions - Video Part II Using Function Notation Part II: Using Function Notation to Solve Expressions

Extend your understanding. . . F(x) “The value of F depends on the value of x” “The value of F is a function of the value of x” In short… “F of x”

Using Function Notation Given f(x) = x – 2, find: a. f(1) = What is the value of “f” when x = 1? F(x) = x – 2 F(x) = (1) – 2 F(x) = -1 b. f(-3) = What is the value of “f” when x = -3? F(x) = x – 2 F(x) = (-3) – 2 F(x) = -5

Using Function Notation Given f(x) = x – 2, find: a. f( ) = What is the value of “f” when x = ? F(x) = x – 2 F(x) = ( ) – 2 F(x) = - 2

Using Function Notation Given g(x) = 3 x, find: a. g(2) = What is the value of “g” when x = 2? g(x) = 3 x g(x) = 3(2) g(x) = 6 Given h(x) = ½ x + 6, find: b. h(6) What is the value of “h” when x = 6? h(x) = ½ x + 6 h(x) = ½ (6) + 6 h(x) = 3 + 6 = 9

Now You Try! 1. Given f(x) = x – 2, find: a. f(10) = F(x) = x – 2 F(x) = (10) – 2 F(x) = 8 b. f(-4) = f(x) = x – 2 f(x) = (-4) – 2 f(x) = -6 c. f(n – 2)= f(x) = x – 2 f(x) = (n – 2) – 2 f(x) = n – 4

Now You Try! 1. Given g(x) = x 2 – 2, find: a. g(10) = g(x) = x 2 – 2 g(x) = (10)2 – 2 g(x) = 98 b. g(-4) = g(x) = x 2 – 2 g(x) = (-4)2 – 2 g(x) = 14 c. g(0)= g(x) = x 2 – 2 g(x) = (0)2 – 2 g(x) = – 2

Applying Function Notation - Video Part III More Function Notation! And you thought we were done with this…

Record Albums Sold in US Year Albums Sold 1973 290 million 1981 280 million 1975 333 million 1985 195 million 1977 345 million 1985 195 million 1979 330 million 1987 178 million What trend or pattern of change do you see in the data in the table? Offer a possible explanation for this trend.

Record Albums Sold in US Year Albums Sold 1973 290 million 1981 280 million 1975 333 million 1985 195 million 1977 345 million 1985 195 million 1979 330 million 1987 178 million The number of albums sold, A, is a function of the year. What information does the following sentence, written in function notation, give about album sales? A(1981) = 280 million Write this in the form “is a function of…”.

Record Albums Sold in US Year Albums Sold 1973 290 million 1981 280 million 1975 333 million 1985 195 million 1977 345 million 1985 195 million 1979 330 million 1987 178 million Explain in words the meaning of each of these symbolic statements: a. A(1973) = 290 million b. A(1987) = 178 million

Record Albums Sold in US Year Albums Sold 1973 290 million 1981 280 million 1975 333 million 1985 195 million 1977 345 million 1985 195 million 1979 330 million 1987 178 million Write the following statement in function notation: “ 330 million albums were sold in 1979”

Record Albums Sold in US Year Albums Sold 1973 290 million 1981 280 million 1975 333 million 1985 195 million 1977 345 million 1985 195 million 1979 330 million 1987 178 million What estimate do you believe is most reasonable for album sales in 1980?