Domains and range

[Tsaren]

Hello guys!

Find the domain and range for each following functions:

a) f(x)=2x-1

b) f(x) = 3

Can you find domain and range without sketching the graph?

And how can you draw f(x)= 3 in a graph - how do we know where the y-intercept and the x-intercept are?

Thank you - appreciate it a lot!

[Slovakov]

Just think of what values can x (domain) and y (range) have so that it is mathematically correct.

For a) you see that both x and y can have any real values, i.e. both the domain and range belong to {-infinity, infinity)

In b)x may have any real value, but f(x) (that is y) is defined as 3. This means that the graph is a horizontal line at y=3. So domain is as in a), while range is just that one element 3.

[alefal]

Just to supplement Slovakov's answer:

f(x)=3 (equal to y=3) is just a straight, horizontal line - it won't have an x-intercept. The y-intercept is already given, a straight, horizontal line at f(x)=3 will always cross the y-axis at 3. The coordinates for f(x)=3 would look like this: (-3, 3), (-2, 3), (-1, 3), (0, 3), (1, 3), (2, 3), (3, 3), (4, 3), etc. The x-axis could be said to be a similar line. The function for the x-axis would be y=0, as it intercepts the y-axis at 0 and is a straight, horizontal line.

You will probably also encounter functions saying something like x=3. These would be straight, vertical lines without an y-intercept, whereas f(x)=3 is a straight, horizontal line without an x-intercept. Here, the value of x is given, instead of the value of y. The y-axis would be an example of such a line, as it can be found at x=0.