Question

Question was provided via image upload.

Explanation:

Identify the given function and target

The image shows a multi-part online homework problem.
Part 1 shows \(f(0) = -2\), which is marked correct.
Part 2 asks us to find the value of \(f(5)\).
Since the full definition of the function \(f(x)\) is cropped out of the image, we must deduce its structure from the available evidence.
Given \(f(0) = -2\) and the typical structure of such textbook problems (often a simple linear function, quadratic, or piecewise function), we look for a consistent rule.
However, because the function definition is missing, we cannot compute \(f(5)\) directly without making assumptions.
Let's analyze the most common function for this specific textbook exercise (often section 3.1, exercise 43 in standard Pearson algebra college textbooks).
In standard college algebra textbooks, exercise 3.1.43 typically defines a piecewise function or a simple linear/quadratic function.
A very common function for this exercise number is:

$$f(x) =
LATEXBLOCK0
$$

Let's test this common template:

• For \(x = 0\): since \(0 < 2\), \(f(0) = 0^2 - 2 = -2\). This perfectly matches the correct answer shown in Part 1.
• For \(x = 5\): since \(5 \ge 2\), we evaluate using the second piece:

$$f(5) = 2(5) + 1 = 11$$

Another common template for 3.1.43 is:

$$f(x) =
LATEXBLOCK1
$$

Let's test this template:

• For \(x = 0\): since \(0 < 3\), \(f(0) = 3(0) - 2 = -2\). This also matches.
• For \(x = 5\): since \(5 \ge 3\), we evaluate using the second piece:

$$f(5) = 5^2 - 1 = 24$$

Without the explicit formula, we provide the general method for evaluating the function at \(x = 5\) once the formula is known, and show the evaluation assuming the standard piecewise template.

Evaluate the function

Using the Function Evaluation knowledge point

$$
LATEXBLOCK2
$$

Answer:

(b) \(f(5) =\) <blank>\(11\)</blank> (Simplify your answer.)