8. Match the description with the correct Function.
Function A:
Function B:
x y
0 1
4 9
8 17
Function C: y=x+20
(4 points)
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Function with the greatest rate of change
Function with the smallest y-intercept
Which function would benefit you the most if it represented your money earned per hour?
Function with the highest initial amount of money
Function A: Function with the highest initial amount of money
Function B: Function with the greatest rate of change
Function C: Function with the smallest y-intercept
Function with the greatest rate of change: Function B (y = x^2 + 1)
Function with the smallest y-intercept: Function C (y = x + 20)
Which function would benefit you the most if it represented your money earned per hour? Function B (y = x^2 + 1)
Function with the highest initial amount of money: Function C (y = x + 20)
Function A: y = x^2 + 1
Function B: y = 2x + 1
Function C: y = x + 20
Function with the greatest rate of change: Function B
Function with the smallest y-intercept: Function A
Which function would benefit you the most if it represented your money earned per hour? Function B
Function with the highest initial amount of money: Function C
To determine the answers to these questions, we need to analyze the given functions and their characteristics.
First, let's calculate the rate of change for each function by finding the difference in y-values divided by the corresponding difference in x-values:
Function A:
Rate of change = (9 - 1) / (4 - 0) = 2
Function B:
Rate of change = (17 - 9) / (8 - 4) = 2
Function C (y=x+20):
Rate of change = (x + 20 - 1) / (x - 0) = 1
From the calculations above, we can see that both Function A and Function B have the same rate of change, which is 2, whereas Function C has a rate of change of 1.
Next, let's examine the y-intercepts of each function:
Function A:
The y-intercept is the y-value when x = 0. In this case, the y-intercept is 1.
Function B:
The y-intercept is the y-value when x = 0. In this case, the y-intercept is 9.
Function C (y=x+20):
The y-intercept is 20, as it represents the value of y when x = 0.
Now, let's analyze the questions one by one:
1. Function with the greatest rate of change:
Both Function A and Function B have the same rate of change, which is 2. Therefore, either Function A or Function B can be considered the answer.
2. Function with the smallest y-intercept:
Among the given functions, Function A has the smallest y-intercept, which is 1.
3. Function that represents money earned per hour:
To determine this, we need to consider the rate of change. Higher rate of change indicates higher earnings per hour. Therefore, Function A and Function B, with a rate of change of 2, would benefit the most if they represent money earned per hour.
4. Function with the highest initial amount of money:
The initial amount of money is represented by the y-intercept. Among the given functions, Function C has the highest initial amount of money, which is 20.
So, to summarize:
1. Function with the greatest rate of change: Both Function A and Function B.
2. Function with the smallest y-intercept: Function A.
3. Function that represents money earned per hour: Either Function A or Function B.
4. Function with the highest initial amount of money: Function C.