Download PreCalc Notes 2-2 Graphing


f(x) = mx + b
linear function

f(x) = b
constant function

f(x) = x2
quadratic function

f(x) = x3
cubic function

f(x) = x
radical function
x
f ( x)
2
32
1
4
0
0
1
4
2
32

If n is even f(x) = xn is similar to the parabola
y = x2.

If n is odd f(x) = xn is similar to that of y = x3.
f ( x)  4  x
x
f ( x)
2
0
1
1.73
0
2
1
1.73
2
0
2
x0
x  4

f ( x)  4  x 2 0<x  2
 x  4 x > 2

x
f ( x)
1
3
0
4
1
3
2
0
3
4
1
0
f ( x)  6 x
x
2
f ( x)
1
12
6
0
0
1
6
2
12

The cost of a long-distance call from Toronto
to Mumbai, India, is 69 cents for the first
minute and 58 cents for each additional
minute (or part of a minute). Draw a graph of
the cost (in dollars) of the phone call as a
function of time (in minutes).
c(t )  0.69
c(t )  0.69  0.58  1.27
c(t )  0.69  2  0.58   1.85
c(t )  0.69  3  0.58   2.43
0  t 1
1 t  2
2t 3
3t  4
t
c(t )
0  t 1
0.69
1 t  2
1.27
2t 3
1.85
3t  4
2.43

Used to determine which curves in the xyplane are functions.

A curve is a function if and only if no vertical
line intersects the curve more than once. (xvalues cannot repeat)

y–
x2 =
2
 x2 + y2 = 4

x + y2 = -5
y  x 2
2
y   x  4
2
y   x  5
Pg 167
#6-16 even, 24, 28-36
even, 42-50 even,
53-54,57,60,60-68 even