Asked by Truth Roberson
The table below represents a linear function.
xx yy
44 77
88 99
1212 1111
1616 1313
Which relationship represents a function with a lesser rate of change than the function represented above?
Ay, equals, one half, x, plus, 4
y=
2
1
x+4
By, equals, 5, x, plus, 3
y=5x+3
C
x
y
D
x
y
Answer
Multiple Choice Answers
AA
BB
CC
DD
xx yy
44 77
88 99
1212 1111
1616 1313
Which relationship represents a function with a lesser rate of change than the function represented above?
Ay, equals, one half, x, plus, 4
y=
2
1
x+4
By, equals, 5, x, plus, 3
y=5x+3
C
x
y
D
x
y
Answer
Multiple Choice Answers
AA
BB
CC
DD
Answers
Answered by
GPT-4o mini
To determine which function has a lesser rate of change than the function represented in the table, we first need to find the rate of change (slope) of the function represented by the given points.
Looking at the points:
- (44, 77)
- (88, 99)
- (1212, 1111)
- (1616, 1313)
We can calculate the rate of change using the formula for slope (m):
\[ m = \frac{\Delta y}{\Delta x} \]
Using the first two points to find the slope:
1. From (44, 77) to (88, 99):
- \(\Delta y = 99 - 77 = 22\)
- \(\Delta x = 88 - 44 = 44\)
- Slope \(m = \frac{22}{44} = \frac{1}{2}\)
This indicates the function represented by the table has a rate of change of \( \frac{1}{2} \).
Now, we will compare this rate of change with the rates of change of the given functions in the options:
A) \( y = \frac{1}{2}x + 4 \)
- Slope = \( \frac{1}{2} \) (same as the original function)
B) \( y = 5x + 3 \)
- Slope = 5 (greater than the original function)
C) This option appears to be incomplete.
D) This option also appears to be incomplete.
Among the options given, the only function with a slope equal to the original function's slope is option A, which does not represent a lesser rate of change.
If we consider the one that definitely has a lesser slope, it would need to be less than \( \frac{1}{2} \). However, none of the provided options (as written) fall into this category aside from noting option A is the same.
Thus, the correct answer for a function with a lesser rate of change is not explicitly listed in complete form. If we only had to choose from the visible choices where distinct rates could be identified, we would conclude **None of the options appear to fit.**
However, the most direct conclusion based on what's presented would be option **A**, since it's equivalent but not lesser. If required, please make sure to verify the completeness of options C and D.
Looking at the points:
- (44, 77)
- (88, 99)
- (1212, 1111)
- (1616, 1313)
We can calculate the rate of change using the formula for slope (m):
\[ m = \frac{\Delta y}{\Delta x} \]
Using the first two points to find the slope:
1. From (44, 77) to (88, 99):
- \(\Delta y = 99 - 77 = 22\)
- \(\Delta x = 88 - 44 = 44\)
- Slope \(m = \frac{22}{44} = \frac{1}{2}\)
This indicates the function represented by the table has a rate of change of \( \frac{1}{2} \).
Now, we will compare this rate of change with the rates of change of the given functions in the options:
A) \( y = \frac{1}{2}x + 4 \)
- Slope = \( \frac{1}{2} \) (same as the original function)
B) \( y = 5x + 3 \)
- Slope = 5 (greater than the original function)
C) This option appears to be incomplete.
D) This option also appears to be incomplete.
Among the options given, the only function with a slope equal to the original function's slope is option A, which does not represent a lesser rate of change.
If we consider the one that definitely has a lesser slope, it would need to be less than \( \frac{1}{2} \). However, none of the provided options (as written) fall into this category aside from noting option A is the same.
Thus, the correct answer for a function with a lesser rate of change is not explicitly listed in complete form. If we only had to choose from the visible choices where distinct rates could be identified, we would conclude **None of the options appear to fit.**
However, the most direct conclusion based on what's presented would be option **A**, since it's equivalent but not lesser. If required, please make sure to verify the completeness of options C and D.