To solve the problem, let's go step by step using the functions provided.

Function $f(x)$

The representation of this function is a table of values where the $x$ values are listed along with their corresponding $f(x)$ values. We will use the provided table for the following evaluations:

1. Evaluate $f(-5)$:

From the table (assuming you have a table for $f(x)$), find the corresponding value of $f(-5)$.

2. Determine $x$ when $f(x) = -3$:

Look for the value of $x$ in the table where $f(x) = -3$.

Function $g(x)$

The function $g(x)$ is given by a set of ordered pairs: $g(x): \{(-16, 27), (-15, -4), (-11, 6), (-10, -14), (10, 43), (50, 75), (51, 68), (65, 17), (72, -15), (74, -10)\}$

3. Evaluate $g(-10)$:

From the given set of ordered pairs, find the value of $g(-10)$. We see that $g(-10) = -14$.

4. Determine $x$ when $g(x) = -15$:

From the ordered pairs, we see that when $g(x) = -15$, $x = 72$.

Function $h(x)$

The function is given as: $h(x) = -3x + 15$

5. Evaluate $h(1)$:

Substitute $x = 1$ into the function $h(x)$: $h(1) = -3(1) + 15 = -3 + 15 = 12$

6. Determine $x$ when $h(x) = 30$:

Set $h(x) = 30$ and solve for $x$: $30 = -3x + 15$ $30 - 15 = -3x$ $15 = -3x$ $x = -5$

Function $p(t)$

The function $p(t)$ is provided as a table with values for $t$ and their corresponding $p(t)$.

7. Evaluate $p(101)$:

From the table, when $t = 101$, we have $p(101) = 85$.

8. Determine $t$ when $p(t) = 44$:

From the table, we see that $p(t) = 44$ when $t = 82$.

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Summary of Results:

1. $f(-5)$ = (from table).
2. $x$ when $f(x) = -3$ = (from table).
3. $g(-10) = -14$.
4. $x = 72$ when $g(x) = -15$.
5. $h(1) = 12$.
6. $x = -5$ when $h(x) = 30$.
7. $p(101) = 85$.
8. $t = 82$ when $p(t) = 44$.

Would you like further explanations on any of these steps?

Related Questions:

1. How do you solve for $x$ in linear equations like $h(x)$?
2. Can you plot the points for $g(x)$ and $p(t)$?
3. What would happen to $h(x)$ if the slope changed?
4. How does interpreting function tables help in real-world situations?
5. Can you convert function $g(x)$ into a graph and analyze it?

Tip:

For function evaluations from tables, always ensure the table is read correctly by matching the input value directly with its corresponding output value.