Alg 3 Functions 1 Algebra 3 Assignment Sheet Functions ...

[Pages:39]Alg 3 Functions

1

Algebra 3 Assignment Sheet

Functions, Fog, Gof, Inverse, Logs

(1) Assignment # 1 ? Functions, Domains

(2) Assignment # 2 ? Composition of Functions

(3) Assignment # 3 ? Inverse Functions

(4) Review Sheet

(5) Quiz

(6) Assignment # 4 ? Exponential Equations

(7) Assignment # 5 ? Logarithms

(8) Assignment # 6 ? Laws of Logarithms

(9) Assignment # 7 ? Laws of Logarithms

(10) Assignment # 8 ? Calculator Logarithms

(11) Review Sheet

(12) TEST

Alg 3 Functions

2

Functions

I Vocabulary a) Function: The set of (x, y) pairs such that____________________________________

____________________________________________________________

b) domain: c) range: Vertical Line Test

II Functions ? A. a) (2,4) (8,1) (8,8)

b) (1,-2) (3,4) (5,-2) c) y = x2 + 5x + 6

d) y = |x|

e) y2 = 8

f) y = x

g) y = -(x + 2)2

h)

f

(x)

=

2x x2 -

4

f(x) is the same as y

Y/N _____ _____ _____ _____ _____ _____

_____ _____

Domain ______________ ______________ ______________ ______________ ______________ ______________

______________ ______________

Alg 3 Functions

3

III Restrictions

1) Denominator 0

5+x , x

2 - 3x , x-5

x x2 + 5x - 6

x

x

x

2) for even roots: negative number

Find the domain of the following please.

a) f (x) = x - 2

b) f (x) = 2x + 5

c) f (x) =

x x-2

d) y = x2 - x -12

e) y =

x2 - 2x - 63 x2 + 8x +15

Alg 3 Functions

4

IV Evaluating functions for y when given a value of x

Evaluating: Substituting in numbers y = x2 + 2x + 3

f (x) = x2 + 2x + 3

f (2) = 22 + 2(2) + 3 = 11

f (-1) = (-1)2 + 2(-1) + 3 = 2

y = f(x)

f (x) = x2 + 2x + 3

1) f (x) = x2 + 2x + 3 f(-1) =

f(0) =

f

1 2

=

2) g(x) = x2 - 2x + 3

Find g(x + 2)

3) If f(x) = x2 - 3x +1 g(x) = x - 5 a) find f(x + 2)

b) find 3f( x) ? g(2x)

c) find f(g(x))

Alg 3 Functions

5

Algebra 3 Assignment # 1

(1) f ( x ) = 3x4 - 16x3 - 7x2 - 28x - 13 , g ( x) = x2 + 2x - 4 . Find each of the following.

(a) g(4)

(c) f (g(-3))

(b) f (6)

(d) The remainder when f ( x ) is divided by ( x - i)

(2) Determine whether each of the following defines y as a function of x. If it is a function, find the domain please.

(a) y = 5x - 4

(f) y = 5 - 4x

(b) y = x2 + 2x - 3 (c) x2 + y2 = 1

(d)

y

=

3x + 5 2x - 3

(e)

y =

x3 + 8 x3 - 7x +

6

(g) y = x2 - 5x - 6

(h)

y

=

x x2 + 1

(i) y =

5 - 2x 3x + 4

(j) y = x3 - 9x2 + 23x - 15

(3) Let the function f be defined by f ( x ) = x + 1. If 2 f () = 20 , find f (3) .

(4) Let the function f be defined by f ( x ) = x + c , where c is constant. If f ( 2) = 10 , find the value of the

constant c.

Alg 3 Functions (1) (a) 20

(b) ?1

(2) (a) Real (b) Not a function

(c) Not a function

(d)

x

3 2

(e) x 1 , 2 , - 3

(3) 28

6 Answers

(c) 27

(d) ?3 ? 12i

(f)

x

5 4

(g) x -1 or x 6

(h) Real

(i)

-

4 3

x

5 4

(j) 1 x 3 or x 5

(4) 8

Alg 3 Functions

7

Composition of Functions

Functions can be added, subtracted, multiplied and divided.

EXAMPLES

1. If f (x) = x2 - 3 and g(x) = 1 find x

a) f(x) + g(x)

b) f(x) g(x)

c) f(x) ? g(x)

d) f(3) g(3)

e) f(3) ? g(3)

Notes:

Let f (x) = x and g(x) = x3 - 3

f g (x) = f(g(x))

Use composition to find the following: If f (x) = x2 - 3 and g(x) = 1 find

x

a) f (x) g(x)

b) g(x) f (x)

If f (x) = 2x -1, g(x)=x2 and h(x)= 1 3x

find f g h(x)

Alg 3 Functions

8

If

f (x)

=

x x

-6 - 4

and g(x)= x+1 x+5

find f g

DOMAIN:

f (x) = x2 + 8x + 15 , and g (x) = x + 3.

If f (x) =

x

1 and g(x)= x2 - 2

find the domain of g f

Find all values of x such that f (g (x)) = g (f ( x)) if

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download