Practice sheet designed to help students evaluate functions like f(x) and g(x) by reading values directly from input-output tables.

Problem Overview:

The task involves evaluating functions from given tables and answering specific questions about the values of the functions. Let's solve each part step by step.

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Part A: Evaluate each function from the table

#### 1)
Given table:
\[
\begin{array}{c|c}
x & f(x) \\
\hline
-4 & 6 \\
2 & 11 \\
7 & 0 \\
10 & 14 \\
\end{array}
\]

Questions:
i) \( f(-4) = \)
ii) \( f(7) = \)

Solution:
- From the table, when \( x = -4 \), \( f(x) = 6 \).
- From the table, when \( x = 7 \), \( f(x) = 0 \).

Answers:
i) \( f(-4) = 6 \)
ii) \( f(7) = 0 \)

---

#### 2)
Given table:
\[
\begin{array}{c|c}
x & f(x) \\
\hline
5 & 37 \\
8 & -13 \\
13 & -55 \\
19 & 22 \\
\end{array}
\]

Questions:
i) \( f(13) = \)
ii) \( f(8) = \)

Solution:
- From the table, when \( x = 13 \), \( f(x) = -55 \).
- From the table, when \( x = 8 \), \( f(x) = -13 \).

Answers:
i) \( f(13) = -55 \)
ii) \( f(8) = -13 \)

---

#### 3)
Given table:
\[
\begin{array}{c|c}
x & f(x) \\
\hline
-17 & -27 \\
-16 & 17 \\
-11 & 1 \\
3 & 29 \\
\end{array}
\]

Questions:
i) \( f(3) = \)
ii) \( f(-17) = \)

Solution:
- From the table, when \( x = 3 \), \( f(x) = 29 \).
- From the table, when \( x = -17 \), \( f(x) = -27 \).

Answers:
i) \( f(3) = 29 \)
ii) \( f(-17) = -27 \)

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#### 4)
Given table:
\[
\begin{array}{c|c}
x & f(x) \\
\hline
0 & -16 \\
4 & 99 \\
10 & 0 \\
14 & -8 \\
\end{array}
\]

Questions:
i) \( f(4) = \)
ii) \( f(14) = \)

Solution:
- From the table, when \( x = 4 \), \( f(x) = 99 \).
- From the table, when \( x = 14 \), \( f(x) = -8 \).

Answers:
i) \( f(4) = 99 \)
ii) \( f(14) = -8 \)

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Part B: Evaluate the functions from the table

#### 1)
Given table:
\[
\begin{array}{c|c|c}
x & f(x) & g(x) \\
\hline
6 & 35 & 19 \\
13 & -19 & 5 \\
15 & 8 & 23 \\
\end{array}
\]

Questions:
i) \( f(13) = \)
ii) \( f(6) = \)
iii) \( f(15) = \)
iv) \( g(13) = \)
v) For what value of \( x \), \( f(x) = 35 \)?
vi) For what value of \( x \), \( g(x) = 5 \)?

Solution:
- From the table, when \( x = 13 \), \( f(x) = -19 \).
- From the table, when \( x = 6 \), \( f(x) = 35 \).
- From the table, when \( x = 15 \), \( f(x) = 8 \).
- From the table, when \( x = 13 \), \( g(x) = 5 \).
- From the table, \( f(x) = 35 \) when \( x = 6 \).
- From the table, \( g(x) = 5 \) when \( x = 13 \).

Answers:
i) \( f(13) = -19 \)
ii) \( f(6) = 35 \)
iii) \( f(15) = 8 \)
iv) \( g(13) = 5 \)
v) \( x = 6 \)
vi) \( x = 13 \)

---

#### 2)
Given table:
\[
\begin{array}{c|c|c}
x & f(x) & g(x) \\
\hline
-6 & -24 & 14 \\
1 & 4 & -4 \\
4 & 16 & 10 \\
\end{array}
\]

Questions:
i) \( f(4) = \)
ii) \( g(1) = \)
iii) \( g(4) = \)
iv) \( f(-6) = \)
v) For what value of \( x \), \( f(x) = -24 \)?
vi) For what value of \( x \), \( g(x) = 4 \)?

Solution:
- From the table, when \( x = 4 \), \( f(x) = 16 \).
- From the table, when \( x = 1 \), \( g(x) = -4 \).
- From the table, when \( x = 4 \), \( g(x) = 10 \).
- From the table, when \( x = -6 \), \( f(x) = -24 \).
- From the table, \( f(x) = -24 \) when \( x = -6 \).
- The table does not show any value of \( x \) for which \( g(x) = 4 \). Therefore, there is no such \( x \).

Answers:
i) \( f(4) = 16 \)
ii) \( g(1) = -4 \)
iii) \( g(4) = 10 \)
iv) \( f(-6) = -24 \)
v) \( x = -6 \)
vi) No value of \( x \)

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Final Answers:

\[
\boxed{
\begin{array}{l}
\text{Part A:} \\
1) \text{i) } 6, \text{ ii) } 0 \\
2) \text{i) } -55, \text{ ii) } -13 \\
3) \text{i) } 29, \text{ ii) } -27 \\
4) \text{i) } 99, \text{ ii) } -8 \\
\\
\text{Part B:} \\
1) \text{i) } -19, \text{ ii) } 35, \text{ iii) } 8, \text{ iv) } 5, \text{ v) } 6, \text{ vi) } 13 \\
2) \text{i) } 16, \text{ ii) } -4, \text{ iii) } 10, \text{ iv) } -24, \text{ v) } -6, \text{ vi) No value} \\
\end{array}
}
\]