The equation given is $4x + 27 = 16$. We are asked to find the range for this equation when the domain is $\{-4, 7, 11\}$.

Step 1: Solve for $x$.

We can first simplify the equation:

$4x + 27 = 16$ $4x = 16 - 27$ $4x = -11$ $x = -\frac{11}{4}$

However, this particular equation was likely used to define the form of the equation, but we don't need to solve it directly for the domain values. Instead, we need to evaluate the function $f(x) = 4x + 27$ for each value in the domain.

Step 2: Evaluate for each $x$ in the domain

The equation we are working with is:

$f(x) = 4x + 27$

• For $x = -4$: $f(-4) = 4(-4) + 27 = -16 + 27 = 11$

• For $x = 7$: $f(7) = 4(7) + 27 = 28 + 27 = 55$

• For $x = 11$: $f(11) = 4(11) + 27 = 44 + 27 = 71$

Step 3: Range

The range for the given domain $\{-4, 7, 11\}$ is $\{11, 55, 71\}$.

None of the answer choices in the image matches this set exactly, so it seems the question may involve further clarification or a misstep in how the range is evaluated.

Would you like more details or help with further clarification?

Here are some related questions:

1. What is the concept of domain and range in a function?
2. How do you solve linear equations step by step?
3. Why do functions have different ranges for different domains?
4. How would the range change if the domain included other values?
5. How do you handle special cases where the range might be undefined?

Tip: Always double-check that you're using the correct function when evaluating a set of domain values to avoid confusion with unrelated equations.