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.
- Slope of Function A: 4
- 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.
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