Function Evaluation, Rule of 4
On the right are four functions, each using one of the function representations we've learned in this lesson.
Use functions,  
f
(
x
)
,
 
g
(
x
)
,
 
h
(
x
)
 
and
 
p
(
t
)
  to answer the questions on the left.
Evaluate  
f
(
−
5
)
 
f
(
−
5
)
=
  

Determine  
x
  when  
f
(
x
)
=
−
3
 
x
=
  

Evaluate  
g
(
−
10
)
 
g
(
−
10
)
=
  

Determine  
x
  when  
g
(
x
)
=
−
15
 
x
=
  

Evaluate  
h
(
1
)
 
h
(
1
)
=
  

Determine  
x
  when  
h
(
x
)
=
30
 
x
=
  

Evaluate  
p
(
101
)
 
p
(
101
)
=
  

Determine  
t
  when  
p
(
t
)
=
44
 
t
=
  	 
f
(
x
)
 


1
2
3
4
5
-1
-2
-3
-4
-5
1
2
3
4
5
-1
-2
-3
-4
-5
x
y


g
(
x
)
 : {(-16,27), (-15,-4), (-11,6), (-10,-14), (10,43), (50,75),
(51,68), (65,17), (72,-15), (74,-10)}

t
 	20	26	28	44	49	62	82	101	105	111
p
(
t
)
 	32	45	101	99	36	25	44	85	74	41

h
(
x
)
=
−
3
x
+
15
 

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 \( t = 82 \).

---

### 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.

Function Evaluation, Rule of 4
On the right are four functions, each using one of the function representations we've learned in this lesson. Use functions f(x), g(x), h(x), and p(t) to answer the questions on the left.
Evaluate f(-5)
f(-5) = 

Determine x when f(x) = -3
x = 

Evaluate g(-10)
g(-10) = 

Determine x when g(x) = -15
x = 

Evaluate h(1)
h(1) = 

Determine x when h(x) = 30
x = 

Evaluate p(101)
p(101) = 

Determine t when p(t) = 44
t = 

This problem explores the evaluation of multiple functions, including f(x), g(x), h(x), and p(t). Learn how to evaluate functions at specific values, solve for variables in linear equations, and interpret sets of ordered pairs. Suitable for students in Grades 8-10.

Math Problem Statement

f ( − 5 )

Determine
x when
f ( x )

x

g ( − 10 )

Determine
x when
g ( x )

x

h ( 1 )

Determine
x when
h ( x )

x

p ( 101 )

Determine
t when
p ( t )

t

h ( x )

Solution

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