Question

Graph the piecewise-defined function

Answer 1

Start by graphing y = |x|. Its vertex is at (0,0), and the graph opens up.

Now translate the entire graph 4 units up. The new vertex will be at (0,4). Draw an empty circle around this point.

Darken the graph of y = |x|+4 ONLY for the part which is left of the y-axis.

Now plot a dark dot at (0,4). Draw a dark, horiz. line from that dot to the right.

That's it!

Answer 2

Answer with explanation:

The function f(x) is given by:

f(x)=  |x|+4, if  x<0

 and    4 ,  if x ≤ 0.

• for x<0

The graph of the function is a strictly decreasing continuous graph i.e. a line with a slope as: -1.

Since, the function f(x) for x<0 is given by:

f(x)= -x+4

also at x=0-    f(x)=4

• Also , for x≥0 the graph of the function is a straight line parallel to the x-axis.

Also, the left hand limit at x=0 is equal to the right hand limit at x=0 is equal to the function's value at x=0.

Hence, the graph of the function is continuous for all the real values.