function A: (0, -4), (1,-2), (0,2), (2,3)
function B: (0,3), (4,-9), (8,-21)
function C: y = x + 5
1. which function has the greatest rate of change (slope)?/______
A. function A
B. function B
C. function C
2. which function has the smallest y-intercept?_________
A. function A
B. function B
C. function C
3. which function would you want to represent your money earned per hour?________
A. function A
B. function B
C. function C
4. which function would give you the highest initial amount of money?__________
A. function A
B. function B
C. function C
1. A. function A (The slope of function A can be calculated as (3-(-4))/(2-0) = 7/2 = 3.5, which is greater than the slopes of function B and C.)
2. B. function B (The y-intercept of function A is -4, the y-intercept of function B is -9, and the y-intercept of function C is 5. -9 is smaller than -4 and 5.)
3. A. function A (Function A represents a rate of change from -4 to 3 over 2 units, which can be interpreted as earnings per hour.)
4. B. function B (The initial amount of money can be determined by looking at the y-intercept. The y-intercept of function A is -4, the y-intercept of function B is -9, and the y-intercept of function C is 5. -9 is the highest initial amount.)
1. To find the rate of change (slope) for each function, we can calculate the slope between two points on each function.
For function A:
The slope between (0, -4) and (1, -2) is (change in y / change in x) = (-2 - (-4)) / (1 - 0) = 2
For function B:
The slope between (4, -9) and (8, -21) is (change in y / change in x) = (-21 - (-9)) / (8 - 4) = -12 / 4 = -3
For function C:
The slope of the line y = x + 5 is equal to 1.
Looking at these values, we can see that the greatest rate of change (slope) is in function A. Therefore, the answer to question 1 is:
A. function A
2. To find the y-intercept for each function, we can look at the point where the function intersects the y-axis (when x = 0).
For function A, the y-intercept is (0, 2).
For function B, the y-intercept is (0, 3).
For function C, the y-intercept is 5, since the equation of the line is y = x + 5.
Comparing these values, we can see that the smallest y-intercept is in function A. Therefore, the answer to question 2 is:
A. function A
3. To represent your money earned per hour, you would want a function that indicates the change in money (y-value) per change in time (x-value).
Among the given functions, function A represents the change in y (money) for a change in x (time). Therefore, the answer to question 3 is:
A. function A
4. "Highest initial amount of money" refers to the y-value when x = 0.
For function A, the initial amount of money is -4.
For function B, the initial amount of money is 3.
For function C, the initial amount of money is 5.
Thus, the highest initial amount of money is in function C. Therefore, the answer to question 4 is:
C. function C
To find the answers to the questions, we need to examine the given functions and analyze their slopes, y-intercepts, and initial amounts. Let's break down each question and determine the correct answer.
1. To find the function with the greatest rate of change (slope), we need to calculate the slope for each function. The slope is determined by the change in y divided by the change in x.
For function A:
Slope of A = (change in y) / (change in x) = (-2 - (-4)) / (1 - 0) = 2 / 1 = 2
For function B:
Slope of B = (change in y) / (change in x) = (-9 - 3) / (4 - 0) = -12 / 4 = -3
For function C:
The slope of function C is given by the coefficient of x, which is 1.
Comparing the slopes, we can see that function A has the greatest rate of change (slope). So, the answer is: A. function A.
2. To determine the function with the smallest y-intercept, we need to compare the y-intercepts of each function. The y-intercept is the point where the function crosses the y-axis (when x = 0).
For function A:
The y-intercept of A is (0, -4).
For function B:
The y-intercept of B is (0, 3).
For function C:
The y-intercept of function C is found by setting x = 0 in the equation: y = x + 5. This gives us y = 0 + 5 = 5.
Comparing the y-intercepts, we can see that function A has the smallest y-intercept. So, the answer is: A. function A.
3. To determine the function that represents money earned per hour, we are looking for a function that has a direct relationship with the independent variable, which is time (hours).
Out of the given functions, function A and function B represent data points rather than an equation. Function C (y = x + 5) represents a linear equation with a slope of 1, indicating that for every hour worked, the earnings increase by $1. Therefore, the answer is: C. function C.
4. To find the function that gives the highest initial amount of money, we need to consider the y-intercepts again.
For function A:
The y-intercept of A is (0, -4).
For function B:
The y-intercept of B is (0, 3).
For function C:
The y-intercept of function C is 5.
Comparing the y-intercepts, we can see that function C (y = x + 5) has the highest initial amount of money. So, the answer is: C. function C.