Algebra 1 Common Core Student Edition, Grade 8-9

Think.........
Use a pencil as a vertical
line. Place the pencil
parallel to they-axis
and slide it across the
graph. See if the pencil
intersects more than one
point at any time.

H o w is th is fu n c tio n

like ones you've seen

before?

The function

w(x) = 250x can be

written as y = 250x.

Remember th a t w(x)

does not mean w times x.

G o t It? 1. I d e n t i f y th e d o m a in a n d ra n g e o f e a c h r e la t io n. R e p re s e n t t h e r e la t io n w it h

a m a p p in g d ia g r a m. Is th e r e la t io n a f u n c t io n?

a. {(4.2,1 .5 ), (5, 2.2), (7, 4.8), (4.2, 0 )} b. {(-1 , 1), (-2 , 2), (4, -4 ), (7, -7 )}

Another way to decide if a relation is a function is to analyze the graph of the relation

u s in g t h e vertical line test. If any vertical line passes through m ore than one point

of the graph, then for some domain value there is more than one range value. So the

relation is not a function.

Ident ifying Functions Using t he Vert ical Line Test

Is the relation a function? Use the vertical line test.

Q { ( — 4 , 2 ) , ( — 3 , 1 ) , (0 , -2), (-4 , -!),(!, 2)} Q y = - x 2 + 3

The dom ain

value - 4

corresponds to

tw o range

values,

2 a n d - 1.

1

j y

: 1 L

X

-2 0

T -1

There is no

vertical line

th a t passes

through more

than one point

of the graph.

(^1) y 1
I \
1
f\^0 X
i "i \
11 v
i
The relation is not a function. The relation is a function.
G o t It? 2. Is th e r e la t io n a f u n c t io n? U s e th e v e r t ic a l l i n e te s t.
a. {(4, 2), (1, 2), (0, 1), (-2 , 2), (3, 3)} b. {(0, 2), (1 -1 ), (- 1 , 4), (0, -3 ), (2 ,1 )}
Y o u h a v e s e e n f u n c t io n s r e p r e s e n te d as e q u a t io n s in v o l v i n g x a n d y, s u c h as
y = -3x + 1. B e lo w is th e s a m e e q u a t io n w r i t t e n u s in g fu n ctio n n o tatio n.
f[x) = —3 x + 1
Notice that f{x) r e p la c e s y. I t is r e a d " / o f x” The le tte r /is th e na m e o f th e fu n c tio n , n o t
a v a r ia b le. F u n c t io n n o t a t i o n is u s e d to e m p h a s iz e t h a t t h e f u n c t i o n v a lu e f(x) d e p e n d s
on the independent variable x. O t h e r le t t e r s b e s id e s / c a n a ls o b e u s e d , s u c h as g a n d h.
Problem 3 Ev a l u a t i n g a Fu n c t i o n
Reading The function w(x) = 250x represents the number of words w(x) you can
read in x minutes. How many words can you read in 8 min?
w(x) = 250x
w{8) = 2 5 0 (8 ) Substitute 8 fo r x.
8 ) = 2 0 0 0 Simplify.
Y o u c a n r e a d 2 0 0 0 w o r d s i n 8 m in.
c
PowerAlgebra.com | Lesson 4 -6 F o rm a liz in g R elations and Functions
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