Question

Function B
x 0 2 4 6
y 2.50 4.03 5.56 7.09

Function C
y = 1.3x + 1
which is greater?

Answer 1

is the graph a function or not a function
x y
4 4
5 5
5 0
7 8
10 1

Answer 2

To compare Function B and Function C, we need to calculate the values of Function C at the same x-values as Function B (0, 2, 4, and 6).

Given Function C:

\[ y = 1.3x + 1 \]

Now we will calculate the corresponding y-values for each x:

1. For \( x = 0 \):
\[
y = 1.3(0) + 1 = 1
\]

2. For \( x = 2 \):
\[
y = 1.3(2) + 1 = 2.6 + 1 = 3.6
\]

3. For \( x = 4 \):
\[
y = 1.3(4) + 1 = 5.2 + 1 = 6.2
\]

4. For \( x = 6 \):
\[
y = 1.3(6) + 1 = 7.8 + 1 = 8.8
\]

Now we can compare the values of Functions B and C for each x:

| x | Function B (y) | Function C (y) |
|---|----------------|----------------|
| 0 | 2.50 | 1 |
| 2 | 4.03 | 3.6 |
| 4 | 5.56 | 6.2 |
| 6 | 7.09 | 8.8 |

Now let's analyze:

- At \( x = 0 \): Function B (2.50) is greater than Function C (1).
- At \( x = 2 \): Function B (4.03) is greater than Function C (3.6).
- At \( x = 4 \): Function C (6.2) is greater than Function B (5.56).
- At \( x = 6 \): Function C (8.8) is greater than Function B (7.09).

In summary, Function B is greater than Function C at \( x = 0 \) and \( x = 2 \), while Function C is greater at \( x = 4 \) and \( x = 6 \). Thus, there is not a single function that is consistently greater across all points.

Answer 3

A relation is considered a function if each input (x-value) maps to exactly one output (y-value). In other words, for every x-value, there should be only one corresponding y-value.

Let's analyze the provided pairs:

- \( (4, 4) \)
- \( (5, 5) \)
- \( (5, 0) \)
- \( (7, 8) \)
- \( (10, 1) \)

In this case, the x-value \( 5 \) corresponds to two different y-values: \( 5 \) and \( 0 \).

Since one input (x = 5) maps to two distinct outputs (y = 5 and y = 0), this relation is **not a function**.