Basics of Functions Continued…

• Domain• Evaluating from…

– An equation– A graph – A table

• Composition– Add/Subtract/Multiply/Divide– Difference Ratio

Domain

2

4(1)

2 3

xf x

x x

2(2) 9g x x

(3) 3 2h x x

2 35. For the functions 2 3 4 1

find the following:

f x x g x x

– 4 – 2 2

5

0

9

4

( )y x f

( )y xg

a.

6. Given the graph, if possible, evaluate (f + g)(1).f(1) = (think when x = 1 on

the f(x) graph, what is the y-value?)

g(1) = (think when x = 1 on the g(x) graph, what is the y-value?)

(f + g)(1) = add the two parts above together

x

y

– 4 – 2 2

5

0

9

4

( )y x f

( )y xg

a.

6. Given the graph, evaluate (f + g)(1).

f(1) = 3 g(1) = 1

(f + g)(1) = 4

x

y

– 4 – 2 2

5

0

9

4

( )y x f

( )y xg

7. Given the graph, if possible, evaluate (f / g)(0).f(0) = (think when x = 0 on

the f(x) graph, what is the y-value?)

g(0) = (think when x = 1 on the g(x) graph, what is the y-value?)

(f / g)(0) = divide

x

y

– 4 – 2 2

5

0

9

4

( )y x f

( )y xg

7. Given the graph, evaluate (f / g)(0).

f(0) = 1

g(0) = 0

(f /g)(0) = 1/0, thus (f/g)(0) is undefined because the denominator

is 0.

x

y

x (x) g(x)

– 2 – 3 undefined

0 1 0

1 3 1

-1 -1 undefined

4 9 2

8. Given the table, if possible, use the given representations of f and g to evaluate (f·g)(1).f(1), when x = 1 in the table, what is the value of f(x)?

g(1), when x = 1 in the table, what is the value of g(x)?

(f · g)(1), evaluate the product

x (x) g(x)

– 2 – 3 undefined

0 1 0

1 3 1

-1 -1 undefined

4 9 2

8. Given the table, if possible, use the given representations of f and g to evaluate (f · g)(1).f(1) = 3

g(1) = 1

(f · g)(1) = 3(1) = 3

x (x) g(x)

– 2 – 3 undefined

0 1 0

1 3 1

-1 -1 undefined

4 9 2

9. Given the table, if possible, use the given representations of f and g to evaluate (f – g)(-2).f(-2), when x =-2 in the table, what is the value of f(x)?

g(-2), when x = -2 in the table, what is the value of g(x)?

(f – g)(-2), evaluate the difference

x (x) g(x)

– 2 – 3 undefined

0 1 0

1 3 1

-1 -1 undefined

4 9 2

9. Given the table, if possible, use the given representations of f and g to evaluate (f – g)(-2).f(-2) = -3

g(-2) = undefined

(f – g)(-2) = undefined

Note: looking back at the graph on slide 7, g(x) is not defined at x = -2. In simplistic terms, that means there is no graph for the value of x.