Question

Which graph represents the piecewise function?

x+3   if  x<0

2x if x ≥ 0

Answer 1

Graph 1 will be the correct one.

Explanation:

We are given the piece wise function defined as

f(x) = x + 3 for x < 0 and f(x) = 2x for x ≥ 0

The first part of the function does not include x = 0.

And, this is in slope-intercept form.

So, slope is 1 i.e. tan Ф = 1, ⇒ Ф = 45°.

And it has y-intercept at (0,3).

So, the conditions are shown in graphs 1 and 3.

Now, the second part of the function equation passes through origin {As the equation is f(x) = 2x}

So, only graph 1 matches both the conditions.

Therefore, graph 1 will be the correct one. (Answer)