Functions and Relations
Determine whether each graph is a function or a relation. How do you know?
2.
1.
3.
4.
6.
5.
8.
7.
9.
Answers:
10.
1. Function
6. Function
2. Relation
7. Relation
3. Function
8. Relation
4. Function
9. Function
5. Relation
10. Relation
WORKING WITH FUNCTIONS
Evaluate each:
1.
If f ( x) = 3x − 5 , find f (3)
2.
If g ( x) = x − 9 , find g (10 )
3.
1
If f ( x) = −4 x + 2 , find f (12), f (−0.5), f ( )
2
Solve for x:
4.
If f ( x) = −3x + 4 and g ( x) = x 2 , find f (x ) = g (−2)
5.
If f ( x) = −2x + 1 and g ( x) = x 2 − 5, find f (x) = g (3)
6.
If f ( x) = −2 x + 4 and g ( x) = x + (−5), find f (x ) = g ( x)
Calculate:
7.
Given f ( x) = −9 x + 3 and g ( x) = x + 5, find f (x ) + g ( x)
8.
Given f ( x) = 2 x − 5 and g ( x) = x + 2, find f (x ) − g ( x)
9.
Given f ( x) = x 2 + 7 and g ( x) = x − 3, find 2 f (x ) + 3g ( x)
ANSWERS:
1. f(3) = 4
2. g(10) = 1
3. f(12) = -46, f(-0.5) = 4, f(1/2) = 0
4. x = 0
5. x = -1/2
6. x = 3
7. -8x + 8
8. x + -7
9. 2x2 + 3x + 5
COMPOSITE FUNCTIONS
Evaluate each composite value:
( f  g )(3)
1.
If f ( x) = 3x − 5 and g ( x) = x 2 , find
2.
If f ( x) = −9 x − 9 and g ( x) = x − 9 , find
( f  g )(10 )
3.
If f ( x) = −4 x + 2 and g ( x) = x − 8 , find
( f  g )(12 )
4.
If f ( x) = −3x + 4 and g ( x) = x 2 , find (g  f )(− 2)
5.
If f ( x) = −2x + 1 and g ( x) = x 2 − 5, find (g  f )(2)
Find each composite:
6.
Given f ( x) = −9 x + 3 and g ( x) = x 4 , find
( f  g )(x )
7.
Given f ( x) = 2 x − 5 and g ( x) = x + 2, find
( f  g )(x )
8.
Given f ( x) = x 2 + 7 and g ( x) = x − 3, find
( f  g )(x )
ANSWERS
1.
( f  g )(3) = f (g (3))
2
g (3) = (3) = 9
f (9) = 3(9) − 5 = 27 − 5 = 22
( f  g )(10) = f (g (10))
2. g (10) = (10) − 9 = 1 = 1
f (1) = −9(1) − 9 = −9 − 9 = −18
( f  g )(12) = f (g (12))
3. g (12) = (12) − 8 = 4 = 2
f (2) = −4(2) + 2 = −8 + 2 = −6
(g  f )(− 2) = g ( f (− 2))
4. f (− 2) = −3(− 2) + 4 = 6 + 4 = 10
2
g (10) = (10) = 100
(g  f )(2) = g ( f (2))
5. f (2) = −2(2) + 1 = −4 + 1 = −3
2
g (−3) = (− 3) − 5 = 9 − 5 =
4=2
6. ( f  g )(x ) = f g (x ) = f (x 4 ) = −9(x 4 ) + 3 = −9 x 4 + 3
7. ( f  g )(x ) = f g (x ) = f (x + 2) = 2(x + 2) − 5 = 2 x + 4 − 5 = 2 x − 1
8. ( f  g )(x ) = f g (x ) = f (x − 3) = (x − 3)2 + 7 = x 2 − 6 x + 9 + 7 = x 2 − 6 x + 16