Question

Function A and Function B are linear functions.
Function A
x y
1 6
2 10
4 18
Function B
y=1/2 x +3
Which statements are true? Select all that apply.

Answer 1

To analyze which statements are true regarding Function A and Function B, we start by determining the equation of Function A based on the given points.

### Function A
The data points for Function A are:
- (1, 6)
- (2, 10)
- (4, 18)

To find the slope (m) of Function A, we can use the following formula between any two points:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's use the points (1, 6) and (2, 10) to calculate the slope:
\[ m = \frac{10 - 6}{2 - 1} = \frac{4}{1} = 4 \]

Now we use point-slope form \( y - y_1 = m(x - x_1) \) to find the equation with the point (1, 6):
\[
y - 6 = 4(x - 1) \\
y - 6 = 4x - 4 \\
y = 4x + 2
\]

With the equation of Function A as \( y = 4x + 2 \), we now compare both functions:

- **Function A equation**: \( y = 4x + 2 \)
- **Function B equation**: \( y = \frac{1}{2}x + 3 \)

### Analyze the statements
Now let's compare the two functions based on their slopes and y-intercepts.

1. **Slope of Function A**: 4
2. **Slope of Function B**: \( \frac{1}{2} \)

Since the slopes are different, they are not parallel.

### Compare y-intercepts:
- **y-intercept of Function A**: 2
- **y-intercept of Function B**: 3

They also have different y-intercepts, hence they are not the same line.

### Conclusion
- Function A is steeper than Function B.
- Function A and Function B are not parallel.
- Function A and Function B are not the same line.

Based on the analysis, the following types of statements about the functions may be true:
- Function A has a greater slope than Function B.
- Function A and Function B are not parallel.
- Function A and Function B intersect at some point (since they are not parallel).

Without the exact statements presented, I can only guide you toward analyzing the truth of potential statements. Please provide the specific statements you want evaluated to determine their validity.