Discovering the characteristics EMA4C
The standard form of a straight line graph is the equationy=mx+c.
Domain and range
The domain isfx:x 2 Rgbecause there is no value ofxfor whichf(x)is undefined.
The range off(x) =mx+cis alsoff(x) :f(x) 2 Rgbecausef(x)can take on any real value.
Intercepts
They-intercept:
Every point on they-axis has anx-coordinate of 0. Therefore to calculate they-intercept, letx= 0.
For example, they-intercept ofg(x) =x 1 is given by settingx= 0:
g(x) =x 1
g(0) = 0 1
= 1This gives the point(0; 1).
Thex-intercept:
Every point on thex-axis has ay-coordinate of 0. Therefore to calculate thex-intercept, lety= 0.
For example, thex-intercept ofg(x) =x 1 is given by settingy= 0:
g(x) =x 1
0 =x 1
)x= 1This gives the point(1; 0).
Sketching graphs of the formy=mx+c EMA4D
In order to sketch graphs of the form,f(x) =mx+c, we need to determine three characteristics:
1.sign ofm
2.y-intercept
3.x-interceptDual intercept method EMA4F
Only two points are needed to plot a straight line graph. The easiest points to use are thex-intercept and the
y-intercept.
Chapter 6. Functions 153