Question

i need help with this question parts d and h

Answer 1

We can see from the question that the graph of the function is as follows:

We can see that this is a piecewise function, and we can see that to find all x for which f(x) = -3, we can proceed as follows:

Part D

1. We can see that the values of the domain of the function for which the function is equal to -3 go from x = 0 until x = 1 (not included). We can conclude this because we have a solid circle that indicates that the function takes this value for x = 0, x = 0.1, and so on. The open circle indicates that the function does not take the value of y = -3 when x = 1.

Therefore, we can conclude that all values of x for which f(x) = -3 are given, in interval notation as follows:

$[0,1)$

Part h

We know that the range of a function is those values for y that we obtain for the function using the domain values of the function.

We can see from the graph that the values of the function go as follows:

$\begin{gathered} (-\infty,0)\rightarrow[0,\infty)\text{ } \\ \\ [0,1)\rightarrow y=-3 \\ \\ [1,\infty)\rightarrow y=[4,\infty) \end{gathered}$

Therefore, we can conclude that the range of the function is, in interval notation as follows:

$[0,\infty)\cup\lbrace-3\rbrace$

Therefore, in summary, we have:

Part D