SOLUTION
From the question, we want to find
(a) The domain of the function.
The domain is gotten from the x-values. Looking at the x-values from the graph whether the curve is expanded or not, it would satisfy infinitely the value of any x-values. That is whatever x-value will make the function defined.
So the domain is all real numbers or negative infinity to positive infinity Written as
[tex]\begin{gathered} (A,B) \\ where\text{ } \\ A=-\infty\text{ and B = }\infty \end{gathered}[/tex](b) The range is the y-values that satisfy the function. Looking at the curve, the y-values would have infinitely number of negative values, but does not exceed 1, which is the maximum value.
So the range is negative infinity to 1.
Written as
[tex]\begin{gathered} (A,B] \\ where\text{ } \\ A=-\infty\text{ and B = 1} \end{gathered}[/tex](c) The function is increasing from infinite negative values of x, up to where x is -3, before it starts decreasing of sloping downwards
Hence the function is increasing between negative infinity to negative 3, written as
[tex]\begin{gathered} (A,B) \\ where\text{ } \\ A=-\infty\text{ and B = -3} \end{gathered}[/tex](d) Interval where f(x) >= 0
For f(x), that is y to be greater than or equal to zero, this must take place at the x-intercept, that is where the graph cuts the x-axis plane. Looking at the graph, this is at -4 and -2
hence the answer is between -4 and -2, written as
[tex]\begin{gathered} [A,B] \\ where\text{ } \\ A=-4\text{ and B = -2} \end{gathered}[/tex]