Question

4.2(2) question 7 thankThe function f(x) = 3(x+15)² - 50

Answer 1

`\begin{gathered} \text{Domain: (-}\infty,\text{ }\infty)\text{ (option D)} \\ \text{Range: \lbrack-50, }\infty)\text{ (option C)} \end{gathered}`

Step-by-step explanation:
`f(x)\text{ = }3\mleft(x+15\mright)^(2)-50`

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

`\begin{gathered} In\text{ interval notation:} \\ \text{Domain: (}-\infty,\text{ }\infty)\text{ (option D)} \end{gathered}`

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

`\text{Range: \lbrack-50, }\infty)\text{ (option C)}`