SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given Quadratic function
[tex]f(x)=-8(x+1)^2-8[/tex]STEP 2: Define the domain and range of a function
We know that the domain of a function is the set of input values for f, in which the function is real and defined. Also, the range of a function comprises the set of values of a dependent variable for which the given function is defined.
STEP 3: Find the domain and the range
Domain: The function has no undefined points nor domain restraints. Therefore, the domain is:
[tex]-\inftyRange: The maximum of the function is given as (-1,-8). Hence, the domain will be less than or equal to the vertex(maximum). This can be written as:[tex]f(x)\leq-8[/tex]Hence, the answers in interval notation will be given as:
[tex]\begin{gathered} Domain:(-\infty,\infty) \\ Range:(-\infty,-8] \end{gathered}[/tex]