F(X) TERMINOLOGYSECTION 4.4

September 20/21, 2010

ACT Opener

1. Solve 2x + 6 – 5x < 15A. x < -3B. x > -3C. x < 3 D. x > 3E. x = -3

2. Solve 7x – 3 > 5x -7F. x > -7G. x < 5H. x > -2I. x < -3J. x = -7

3. Solve the system using Cramer’s Rule. 5x – 8y = -106x + 12y = 6

f(x) Terminology

f(x) It is pronounced “f of x” It means “the value of y in function f, where

the independent variable is x.” Any letter may be used for the name of a

function f(x) terminology allows us to show what

value is being substituted for x.

f(x) Terminology

y = -7x + 100

f(x) = -7x + 100

Function name

Variable used in function

Examples: Let f(x) = -7x+1001. f() f() = -7() + 100

2. f(7)f(7) = -7(7) + 100f(7) = -49 + 100f(7) = 51

Examples:Let f(x) = x + 25 and g(x) = x2 – 5x3.

4. f(f(6))= f( (6)+25 )= f( 31)= (31) + 25= 56

)2(

)2(

f

g25)2(

)2(522

27

104

27

6

9

2

Pronounced “f of f of 6”

Examples:Let f(x) = x + 25 and g(x) = x2 – 5x5. f(g(1))

=f((1)2 – 5(1))=f(1 - 5)=f(-4)= (-4) + 25=21

6. f(q)f(q) = q + 25

7. f(g(k))= f((k)2 – 5(k))= f(k2 – 5k)= (k2 – 5k)+25= k2 – 5k+25

Examples:Let f(x) = x + 25 and g(x) = x2 – 5x8. g(f(L))

= g(L + 25)= (L + 25)2 – 5(L + 25)= (L + 25)(L + 25) – 5L – (5)(25)= L2 + 50L + 625 – 5L – 125= L2 + 45L + 500

Examples

Page 131 #28 t = number of minutes since they left

boatdock f(t) = number of meters they are away

from boatdock on the way out g(t) = number of meters they are away

from boatdock on the way back in

Page 131 #28

A. f(t) = 32tf(3) f(7) f(10)f(3) = 32(3) f(7) = 32(7) f(10) = 32(10)f(3) = 96 f(7) = 224 f(10) = 320

B. g(t) = -17t + 510g(18) g(23)g(18) = -17(18) + 510 g(23) = -17(23) + 510g(18) = 204 g(23) = 119

Page 131 #28

C.)

10 20 30t

100

200

300

400

f(t) or g(t)

gf

(10.41, 333.12)

Page 131 #28

D.) f(t) = g(t) 32t = -17t + 510

+17t + 17t49t = 51049 49t = 10.41 minutes

f(10.41) = 32(10.41)f(10.41) = 333.12 meters

E) At the point where the graphs intersect, the boat was turning around.

Page 131 #28

F) g(t) = 00 = -17t + 510-510 -510-510 = -17t-17 -17t = 30 minutes

Exit Slip

Let f(x) = 3x + 11 and g(x) = x2 + x + 1 Evaluate the following: 1. f(-5)2. g(f(-5))