Question

What is this question trying to ask and why is c the correct answer?

Answer 1

Answer: (C) 1

Step-by-step explanation:

The question is asking which y-value are not represented in the graph.  IN other words, they are asking for which values are not included in the range.

You can do this by graphing the equations:

y = x + 2    for x ≥ 0     has a y-intercept of +2 with y-values increasing

• Note: +2 is included so has an closed dot

y = x - 2     for x < 0     has a y-intercept of -2 with y-values decreasing

• Note: -2 is not included so has an open dot

Therefore, there are no y-values between +2 and -2 (including -2). The only option provided between these values is 1, which is option C.

Answer 2

Step-by-step explanation:

The given function is an increasing piecewise function with a jump at x=0 from

f(0-) = -2 to f(0)=+2.

Hence values of f(x) in the interval (-2,+2] cannot be achieved, since

for all x<0, f(x)<-2, and

for all x>=0, f(x)>= +2.

See attached graph for visual explanation.