Two input-output pairs for function f(x) are (−6,52) and (−1,172). Two input-output pairs for function g(x) are (2,133) and (6,−1) . Paige says that function f(x) has a steeper slope. Formulate each function to assess and explain whether Paige's statement is correct.(4 points)
Math Short Answer Rubric (4 points)
Points Awarded Criteria
4
The answer is clear and correct.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
3
The answer is mostly correct. The student made small errors while solving.
The answer shows that the student used some problem-solving skills and reasoning.
Most work is shown or explained.
2
The answer is partially correct. The student made errors while solving.
The answer shows that the student used some problem-solving skills or reasoning.
Some work is shown or explained.
1
The answer is incorrect. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Little or no work is shown.
0 The question is not answered.
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To assess whether Paige's statement is correct, we need to compare the slopes of the two functions.
To find the slope of a function, we can use the formula:
slope = (change in output) / (change in input)
For function f(x):
(change in output) = 172 - 52 = 120
(change in input) = -1 - (-6) = 5
slope of f(x) = 120/5 = 24
For function g(x):
(change in output) = -1 - 133 = -134
(change in input) = 6 - 2 = 4
slope of g(x) = -134/4 = -33.5
Comparing the slopes, we see that the slope of f(x) is 24 and the slope of g(x) is -33.5.
Therefore, Paige's claim is incorrect. The function g(x) actually has a steeper slope.