4-1 Identifying Linear Functions And 4-2 Using Intercepts

1. #16, p. 234

Yes, it is a function; yes, it is linear

Yes, it is a function; no, it is not linear

No, it is not a function

The given answer states that the given object is both a function and linear. This means that there is a one-to-one correspondence between the input and output values, and the relationship between the input and output values follows a linear pattern.

Explanation

The given answer states that the given object is both a function and linear. This means that there is a one-to-one correspondence between the input and output values, and the relationship between the input and output values follows a linear pattern.

2. #14, p. 240

X-int.: −5; y-int.: −1

X-int.: −4; y-int.: 1

X-int.: −1; y-int.: −5

Not here

The correct answer is x-int.: −5; y-int.: −1. This means that the graph of the equation intersects the x-axis at -5 and the y-axis at -1.

Explanation

The correct answer is x-int.: −5; y-int.: −1. This means that the graph of the equation intersects the x-axis at -5 and the y-axis at -1.

3. #20, p. 234

Yes, it is a linear function. There is a constant rate of change.

No, it is not a linear function. There is not a constant rate of change.

The given answer states that the function is linear because it has a constant rate of change. In a linear function, the rate of change between any two points on the graph is always the same. This means that as the input (x) increases by a certain amount, the output (y) also increases by a consistent amount. Therefore, the function can be considered linear.

Explanation

The given answer states that the function is linear because it has a constant rate of change. In a linear function, the rate of change between any two points on the graph is always the same. This means that as the input (x) increases by a certain amount, the output (y) also increases by a consistent amount. Therefore, the function can be considered linear.

4. #22, p. 240 graph only

Not here

not-available-via-ai

Explanation

not-available-via-ai

5. #18, p. 240

X-int.: 2; y-int.: −2

X-int: −2; y-int.: 6

X-int: −8; y-int.: 2

Not here

The correct answer is x-int: −8; y-int.: 2. This means that the graph of the equation crosses the x-axis at -8 and the y-axis at 2.

Explanation

The correct answer is x-int: −8; y-int.: 2. This means that the graph of the equation crosses the x-axis at -8 and the y-axis at 2.

6. #26, p. 241

Not here

not-available-via-ai

Explanation

not-available-via-ai

7. #18, p. 234

Yes, it is a linear function. There is a constant rate of change.

No, it is not a linear function. There is not a constant rate of change.

The given answer is correct because a linear function is characterized by a constant rate of change. In this case, it is stated that there is not a constant rate of change, indicating that the function is not linear.

Explanation

The given answer is correct because a linear function is characterized by a constant rate of change. In this case, it is stated that there is not a constant rate of change, indicating that the function is not linear.

8. #36, p. 241

Graph A

Graph B

Graph C

Graph D

not-available-via-ai

Explanation

not-available-via-ai

9. #28, p. 235

Yes, it is a function; yes, it is linear

Yes, it is a function; no, it is not linear

No, it is not a function

The given answer states that the given entity is a function, meaning that each input has a unique output. However, it is not linear because it does not satisfy the property of linearity, which requires the function to have constant rates of change. Therefore, the given entity is a function but not a linear one.

Explanation

The given answer states that the given entity is a function, meaning that each input has a unique output. However, it is not linear because it does not satisfy the property of linearity, which requires the function to have constant rates of change. Therefore, the given entity is a function but not a linear one.