Function A:
graph points : (0,-4), (1,-2), (0,2), (3,2)
Function B:
0
3
4
-9
Function C. y = x + 5
8
-21
(4 points)
a. Which function has the greatest rate of change (slope)?
b. Which function has the smallest y-intercept?
e. Which function would you want to represent your money camed per hour?
4. Which function would give you the highest intial amount of money?
a. Function C has the greatest rate of change (slope) because it is a linear function with a slope of 1.
b. Function A has the smallest y-intercept because it passes through the point (0,-4), which is the lowest y-value among all the given points.
e. Function C (y = x + 5) would be the most appropriate to represent money earned per hour because it has a linear relationship and the slope of 1 represents a constant increase in money for each hour worked.
4. Function C (y = x + 5) would give you the highest initial amount of money because it has a y-intercept of 5, which represents the starting amount of money.
a. To determine the function with the greatest rate of change (slope), we need to calculate the slopes for each function.
For Function A:
Slope = (change in y) / (change in x)
Slope = (2 - (-4)) / (3 - 0) = 6 / 3 = 2
For Function B:
Since B is a horizontal line, the slope is 0.
For Function C (y = x + 5):
The slope is the coefficient of x, which is 1.
Comparing the slopes, we can see that Function A has the greatest rate of change (slope).
b. The y-intercept is the value of y when x is equal to zero.
For Function A:
y-intercept = -4
For Function B:
y-intercept = 0
For Function C:
y-intercept = 5
Comparing the y-intercepts, we can see that Function B has the smallest y-intercept.
e. To represent money earned per hour, you would want a function that has a constant rate of change (slope) since we earn money per hour. This means that the slope should not change over time.
Function B has a slope of 0, indicating a constant rate of change. Therefore, Function B would be the one that represents money earned per hour.
4. To determine the function that would give you the highest initial amount of money, we need to look at the y-intercepts.
Comparing the y-intercepts:
For Function A:
y-intercept = -4
For Function B:
y-intercept = 0
For Function C:
y-intercept = 5
Among the three functions, Function C (y = x + 5) has the highest initial amount of money since its y-intercept is the highest at 5.
To determine the answers to the given questions, we need to assess the properties of the functions. Let's break it down step by step:
Function A:
- In order to find the slope (rate of change), we need to calculate the difference in y-values divided by the difference in x-values for any two points on the graph.
- Using the given points, we can calculate the slopes between each two points:
- Slope between (0,-4) and (1,-2) = (-2 - (-4)) / (1 - 0) = 2/1 = 2
- Slope between (0,-4) and (0,2) = (2 - (-4)) / (0 - 0) = 6/0 = undefined (vertical line)
- Slope between (1,-2) and (0,2) = (2 - (-2)) / (0 - 1) = 4/-1 = -4
- Slope between (0,2) and (3,2) = (2 - 2) / (3 - 0) = 0/3 = 0
- Therefore, the function with the greatest rate of change (slope) is Function A between the points (0,-4) and (1,-2) with a slope of 2.
- To find the y-intercept, we need to locate where the graph of the function intersects the y-axis.
- Looking at the given graph, we can see that Function A intersects the y-axis at -4, which is the smallest y-intercept among the provided options.
Function B:
- There is no equation provided for Function B; instead, we are given a list of numbers. Without an equation, we cannot determine the rate of change (slope) or the y-intercept for this function.
Function C: y = x + 5
- The equation of Function C is given as y = x + 5. In this case, the slope and y-intercept are explicitly defined by the equation.
- The slope of the function is the coefficient of x, which is 1. Therefore, the rate of change for Function C is 1.
- The y-intercept is the constant term, which is 5. Thus, the y-intercept for Function C is 5.
Based on the information from the equations and points, we can answer the remaining questions:
c. To represent your money earned per hour, you would want a function with a constant rate of change (slope) since you would want a fixed amount of money earned per hour. In this case, Function C (y = x + 5) has a rate of change of 1, making it the appropriate choice.
d. The "highest initial amount of money" refers to the y-intercept, as it represents the starting value of the function. Looking at the y-intercepts of Functions A, B (not determined), and C, we can see that Function C has the highest initial amount of money at 5.
To summarize:
a. Function A has the greatest rate of change (slope) between the points (0,-4) and (1,-2).
b. Function A has the smallest y-intercept (-4).
c. Function C (y = x + 5) would best represent money earned per hour.
d. Function C (y = x + 5) would give you the highest initial amount of money (5).