[tex]\begin{gathered} \text{Domain: (-}\infty,\text{ }\infty)\text{ (option D)} \\ \text{Range: \lbrack-50, }\infty)\text{ (option C)} \end{gathered}[/tex]
Explanation:[tex]f(x)\text{ = }3\mleft(x+15\mright)^{2}-50[/tex]
Domain are the inputs of the function. They are the x values of the function
The function gives a parabola. This means the values of x will be from negative infinty to positve infinity
[tex]\begin{gathered} In\text{ interval notation:} \\ \text{Domain: (}-\infty,\text{ }\infty)\text{ (option D)} \end{gathered}[/tex]
Plotting the graph:
Range are the outputs of the function. They are the y values of the function
From the graph, we see tip of the parabola starts at y = -50 and extends upwards
The y value will be from -50 to positive infinity
[tex]\text{Range: \lbrack-50, }\infty)\text{ (option C)}[/tex]
