Question

What is the domain of this function? (assume there are arrows at the ends of the graph) The answer has the form [A, B] Where A = and B = What is the range of this function? The answer has the form Select an answer Where A = and B = On what interval is the function increasing? The answer has the form Select an answer Where A = and B = On what interval is f(x) >= 0? The answer has the form Select an answer Where A = and B =

Answer 1

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

`\begin{gathered} (A,B) \\ where\text{ } \\ A=-\infty\text{ and B = }\infty \end{gathered}`

(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

`\begin{gathered} (A,B] \\ where\text{ } \\ A=-\infty\text{ and B = 1} \end{gathered}`

(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

`\begin{gathered} (A,B) \\ where\text{ } \\ A=-\infty\text{ and B = -3} \end{gathered}`

(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

`\begin{gathered} [A,B] \\ where\text{ } \\ A=-4\text{ and B = -2} \end{gathered}`