To solve $g(-8) \cdot h(-3)$ in simplified form, we need to find $g(-8)$ and $h(-3)$ separately.

Step 1: Determine $g(-8)$

From the table provided:

• When $x = -8$, $g(x) = -10$. Thus, $g(-8) = -10$.

Step 2: Determine $h(-3)$

From the graph of $h(x)$:

• When $x = -3$, the value of $h(x)$ is $9$ (based on the graph's y-coordinate at $x = -3$). Thus, $h(-3) = 9$.

Step 3: Calculate $g(-8) \cdot h(-3)$

Now that we have $g(-8) = -10$ and $h(-3) = 9$, we can find: $g(-8) \cdot h(-3) = (-10) \cdot 9 = -90$

Final Answer

$g(-8) \cdot h(-3) = -90$

Would you like further clarification or have any questions?

Related Questions:

1. How would the result change if $g(-5) \cdot h(-3)$ was calculated instead?
2. What is the interpretation of the function $f(x) = -x$ given here?
3. How can we determine if $h(x)$ represents a quadratic function from its graph?
4. What is the product $g(-5) \cdot h(-5)$ based on the information provided?
5. How would we find $g(5) \cdot h(-1)$?

Tip: When solving problems involving function tables and graphs, break down each function separately to avoid mixing values.