The problem provides the equation for a function:

$f(x) = -3x^2 + 5x - 2$

We are tasked with finding the corresponding dependent value $f(x)$ for values of $x$ chosen from the set { -3, -2, -1, 0, 1 }.

Let’s substitute each value of $x$ into the equation and calculate the corresponding $f(x)$ for each.

Substituting $x = -3$:

$f(-3) = -3(-3)^2 + 5(-3) - 2 = -3(9) - 15 - 2 = -27 - 15 - 2 = -44$

Substituting $x = -2$:

$f(-2) = -3(-2)^2 + 5(-2) - 2 = -3(4) - 10 - 2 = -12 - 10 - 2 = -24$

Substituting $x = -1$:

$f(-1) = -3(-1)^2 + 5(-1) - 2 = -3(1) - 5 - 2 = -3 - 5 - 2 = -10$

Substituting $x = 0$:

$f(0) = -3(0)^2 + 5(0) - 2 = -2$

Substituting $x = 1$:

$f(1) = -3(1)^2 + 5(1) - 2 = -3(1) + 5 - 2 = -3 + 5 - 2 = 0$

Now, let's review the choices:

• $f(-3) = -44$
• $f(-2) = -24$
• $f(-1) = -10$
• $f(0) = -2$
• $f(1) = 0$

Among the provided options, the closest corresponding dependent value is -2 (for $x = 0$).

Answer:

• The correct answer is -2.

Would you like more detailed steps or have any questions? Here are some related questions to explore:

1. How do we evaluate a function for different values of $x$?
2. What happens if the coefficient of $x^2$ in the function changes?
3. Can the quadratic function have a different set of values for $x$?
4. How would the graph of this function look like?
5. What are other types of functions that could be solved similarly?

Tip: Always substitute each value of $x$ directly into the equation and simplify step by step!