4 3 2 (^1) 1 1 2 3 4
1
2
3
4
5
6
7
8
9
10
0
( 1; 1)
( 2; 4)
( 3; 9)
(1; 1)
(2; 4)
(3; 9)
B A
x
y
Step 3: Determine the domain and range
Domain:x 2 R
From the graph we see that for all values ofx,y 0.
Range:fy:y 2 R; y 0 g
Step 4: Find the axis of symmetry
fis symmetrical about they-axis. Therefore the axis of symmetry offis the linex= 0.
Step 5: Determine thex-value for whichf(x) = 6^14
f(x) =
25
4
)
25
4
=x^2x=±5
2
=± 2
1
2
See pointsAandBon the graph.
Step 6: Determine the intercept
The functionfintercepts the axes at the origin(0; 0).
We notice that as the value ofxincreases from 1to 0,f(x)decreases.
At the turning point(0; 0),f(x) = 0.
As the value ofxincreases from 0 to∞,f(x)increases.
Chapter 6. Functions 159