Question

Please help me-

On a piece of paper, graph f(x) = {6 if -5 < x < -1
{4 if -1 < x < 2
{2 if 2< x < 5 .
Then determine which
answer choice matches the graph you drew.

Answer 1

Answer: Choice A

Explanation:

You are basically graphing the three horizontal lines y = 6, y = 4 and y = 2; however, there are restrictions to each line.

• The first line (y = 6) is only graphed when $-5 < x \le -1$
• The second line (y = 4) is only graphed when $-1 < x \le 2$
• The third line (y = 2) is only graphed when $2 < x \le 5$

That's how we get the staircase pattern as shown in graph A. This is considered a piecewise function since we're graphing pieces of various other functions.

Note the use of open holes vs closed circles for the endpoints. The open holes correspond to parts of the inequality that don't have "or equal to", which means we leave that part out of the graph. In contrast, the closed fill in circles do have "or equal to" associated with them, so we do include those endpoints.