What is the domain of this:?

Question

f(x) = 3x if x does not equal 0

4 if x=0

and how do you graph it?

Answer 1

this function is defined for all real x...the graph is a straight horizontal line with a jump discontinuity at x=0

Answer 2

y = 3x

y = mx + b where m is slope and b is y-intercept

draw a graph with slope 3 and y-int 0, with a hole in it (open circle) where x = 0

and draw a point at (0, 4)

scan left to right to see what values of x are covered in this graph - all values of x are on the graph so the domain is all real numbers

Answer 3

f(x) = 3x is a line with a slope of 3; that is, for every unit increase of the x (in the x-axis), the corresponding increase of the f(x) (or y in the y-axis) is 3*x.

A sample set of points would be {(1,3), (-1,-3), (2, 6), (-2, -6)}.

As for the second condition, the line will skip (0,0); that is, there will be a hole in (0,0), and instead have a point in (0,4).

Answer 4

the Domain is All Real Numbers except 0

otherwise expressed x = (-infinity,0), (0, infinity)

the graph looks like the graph of y = 3x, a graph going through the origin with slope of 3. Except when x=0, the y value is at 4. So there's a discontinuity in the function, so draw a hole at the origin and a point at (0,4).