Question
The table shown at the right gives y as a function of x, that is, yequalsf(x). Use the table to answer parts a through d below.
x
negative 9
negative 5
negative 7
7
13
21
26
y equals f left parenthesis x right parenthesis
2
5
7
1
10
9
14
a. Is negative 5 an input or an output of this function?
b. Is f (negative 5) an input or an output of this function?
c. State the domain and range of this function.
d. Explain why this relationship describes y as a function of x.
x
negative 9
negative 5
negative 7
7
13
21
26
y equals f left parenthesis x right parenthesis
2
5
7
1
10
9
14
a. Is negative 5 an input or an output of this function?
b. Is f (negative 5) an input or an output of this function?
c. State the domain and range of this function.
d. Explain why this relationship describes y as a function of x.
Answers
GPT-4o mini
To answer the questions based on the given function \( y = f(x) \) represented by the table, we will analyze the values provided.
### a. Is -5 an input or an output of this function?
- **Answer**: -5 is an **input** of this function. In the context of functions, the inputs correspond to the \( x \) values, and -5 is listed under the \( x \) column.
### b. Is \( f(-5) \) an input or an output of this function?
- **Answer**: \( f(-5) \) is an **output** of this function. The expression \( f(-5) \) represents the value of the function when the input is -5, which corresponds to the \( y \) value in the table.
### c. State the domain and range of this function.
- **Domain**: The set of inputs (or \( x \) values) from the table: \{ -9, -5, -7, 7, 13, 21, 26 \}.
- **Range**: The set of outputs (or \( y \) values) from the table: \{ 2, 5, 7, 1, 10, 9, 14 \}.
### d. Explain why this relationship describes \( y \) as a function of \( x \).
- **Answer**: This relationship describes \( y \) as a function of \( x \) because, for every unique input (value of \( x \)), there is exactly one corresponding output (value of \( y \)). In other words, each \( x \) value from the domain maps to a single \( y \) value in the range, which satisfies the definition of a function. For example, in the table, when \( x = -5 \), \( y \) is uniquely defined as 5. There are no \( x \) values that result in multiple \( y \) values.
### a. Is -5 an input or an output of this function?
- **Answer**: -5 is an **input** of this function. In the context of functions, the inputs correspond to the \( x \) values, and -5 is listed under the \( x \) column.
### b. Is \( f(-5) \) an input or an output of this function?
- **Answer**: \( f(-5) \) is an **output** of this function. The expression \( f(-5) \) represents the value of the function when the input is -5, which corresponds to the \( y \) value in the table.
### c. State the domain and range of this function.
- **Domain**: The set of inputs (or \( x \) values) from the table: \{ -9, -5, -7, 7, 13, 21, 26 \}.
- **Range**: The set of outputs (or \( y \) values) from the table: \{ 2, 5, 7, 1, 10, 9, 14 \}.
### d. Explain why this relationship describes \( y \) as a function of \( x \).
- **Answer**: This relationship describes \( y \) as a function of \( x \) because, for every unique input (value of \( x \)), there is exactly one corresponding output (value of \( y \)). In other words, each \( x \) value from the domain maps to a single \( y \) value in the range, which satisfies the definition of a function. For example, in the table, when \( x = -5 \), \( y \) is uniquely defined as 5. There are no \( x \) values that result in multiple \( y \) values.