Pr o b l em 1 Classif ying Functions as Linear or Nonlinear

Pizza The area A, in square inches, of a pizza is a function of its radius r, in inches.

The cost C, in dollars, of the sauce for a pizza is a function of the weight w, in ounces,

of sauce used. Graph these functions shown by the tables below. Is each function

linear o r nonlinear?

Pizza Area Sauce Cost

21 2.57

4 50.27

61 13.10

8 201.06

10 314.16

The relationships shown in

the tables are functions.

Need

(^2) $.80
4 $1.60
6$2.40
8$3.20
10 $4.00
Pl an
To classify the functions as Use the tables to make
linear or nonlinear graphs.
Lk
How can a graph tell
y o u i f a fu n c tio n is
linear or nonlinear?
The graph of a linear
function is a nonvertical
line or part of a line, but
the graph of a nonlinear
function is not.
Graph A as a fu n c tio n o f r.
Pizza Area
Graph C as a function of w.
Sauce Cost
4 6 £
Radius (in.), r
f
Use th e vertical
axis for A, the
dependent variable.
6
i—ru ^
O
S 2o
u
r\
Use th e ho rizo n ta l
axis for r, the
independent variable. ” 0^2 4 6 8 10
T h e g r a p h is a c u rv e , n o t a l in e , s o th e
fu n c tio n is nonlinear.
The graph is a line, so the
fu n ctio n is linear.

Got It? 1. a. T h e t a b le b e lo w s h o w s th e f r a c t io n A o f th e o rig in a l area o f a piece o f
p a p e r t h a t r e m a in s a fte r t h e p a p e r h a s b e e n c u t i n h a l f n t im e s. G r a p h th e
f u n c t i o n r e p r e s e n te d b y t h e ta b le. Is t h e f u n c t i o n linear or nonlinearl
r ... - ................... ..... ..................................................i
Cutting Paper
Number of Cuts, n
..|
1
.........
234
Fraction of Original Area Remaining, A^124118161
b. Reasoning Will the area A in p a r t (a ) e v e r re a c h zero? E x p la in.
c
PowerAlgebra.com Lesson 4-3 Patterns and N o n lin ear Functions^247