Question

With the help of the graph above, find the domain and range of the function $g\left(x\right)$.

• A. Domain: $g\left(x\right)\ge 4$; Range : all real numbers
• B. Domain: $g\left(x\right)\le 4$; Range : all real numbers
• C. Domain: all real numbers; Range : $g\left(x\right)\ge 4$
• D. Domain: all real numbers; Range: $g\left(x\right)\le 4$

Answer 1

The correct option is D Domain: all real numbers; Range: $g\left(x\right)\le 4$

The domain for the above function is all real numbers.

Now consider the range.

For all $x<-3$ $g\left(x\right)<4$ and for all $x\ge -3$ $g\left(x\right)\le 4$.

Hence, $g\left(x\right)ϵ(-\infty ,4]$