Let's work through the question visible in your image.

We are given the function $f(x) = x^2 + 5x + 2$. The task is to compute two expressions:

1. $f(-3) + f(5)$
2. $f(-3) - f(5)$

Step 1: Calculate $f(-3)$

Substitute $x = -3$ into the function: $f(-3) = (-3)^2 + 5(-3) + 2 = 9 - 15 + 2 = -4$

Step 2: Calculate $f(5)$

Substitute $x = 5$ into the function: $f(5) = (5)^2 + 5(5) + 2 = 25 + 25 + 2 = 52$

Step 3: Compute $f(-3) + f(5)$

Now, sum the values of $f(-3)$ and $f(5)$: $f(-3) + f(5) = -4 + 52 = 48$

Step 4: Compute $f(-3) - f(5)$

Now, subtract $f(5)$ from $f(-3)$: $f(-3) - f(5) = -4 - 52 = -56$

Final Answers:

• $f(-3) + f(5) = 48$
• $f(-3) - f(5) = -56$

Let me know if you'd like any further details or explanations!

Here are five related questions for further practice:

1. What is $f(0) + f(1)$ for the same function $f(x) = x^2 + 5x + 2$?
2. Calculate $f(2)$ and $f(-2)$, and find the sum $f(2) + f(-2)$.
3. If $f(x) = x^2 + 5x + 2$, what are the values of $f(4)$ and $f(-4)$?
4. How does the function behave as $x \to \infty$? What is the general form of the graph?
5. For what values of $x$ does $f(x) = 0$?

Tip:

Always double-check your algebraic substitutions carefully, especially with negative numbers, to avoid sign errors.