To solve the expression $-2g(-7) + 3h(0)$ in simplified form, we need to find the values of $g(-7)$ and $h(0)$ from the given information.

Step 1: Evaluate $g(-7)$

From the table provided: $g(-7) = -9$

Step 2: Evaluate $h(0)$

The function $h(x)$ is defined as: $h(x) = -x + 3$ Substitute $x = 0$: $h(0) = -0 + 3 = 3$

Step 3: Substitute into the Expression

Now, substitute the values of $g(-7)$ and $h(0)$ into the expression: $-2g(-7) + 3h(0) = -2(-9) + 3(3)$ Calculate each part: $-2(-9) = 18$ $3(3) = 9$ So, $18 + 9 = 27$

Final Answer

The simplified form of $-2g(-7) + 3h(0)$ is: $\boxed{27}$

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. How would the result change if the expression was $-3g(-7) + 4h(0)$?
2. What is the value of $f(x)$ at $x = -7$ based on the graph?
3. Can we generalize $h(x) = -x + 3$ for any other values to find similar expressions?
4. How does changing $x$ in $h(x)$ affect the outcome in expressions like this?
5. What if we considered another function, $k(x)$, and added it to the expression?

Tip: Always double-check function definitions and table values to ensure accurate substitutions in expressions.