match the description with the correct function
function A:
(0,-2), (4,-1), and (8,0)
function B:
(1, 0), (4, 9), and (8, 17)
function C:
y = x + 20
1. function with the greatest rate of change _____
2. function with the smallest y-intercept _______
3. which function would benefit you the most if it represented your money earned per hour _______
A. function A
B. function B
C. function C
1. function with the greatest rate of change: B (function B)
2. function with the smallest y-intercept: A (function A)
3. which function would benefit you the most if it represented your money earned per hour: C (function C)
1. The function with the greatest rate of change is function C (y = x + 20). Since the coefficient of x is 1, the rate of change or slope of the function is 1.
2. The function with the smallest y-intercept is function A. The y-intercept is the value of y when x = 0. In function A, the value of y when x = 0 is -2.
3. The function that would benefit you the most if it represented your money earned per hour is function C (y = x + 20). This function represents a linear relationship where the earnings increase by $1 for every hour worked, as indicated by the coefficient of x, which is 1.
To match the descriptions with the correct functions, we need to analyze the given information about each function. Let's look at each description and determine the corresponding function.
1. The rate of change of a function is determined by how steeply it climbs or descends. We can calculate the rate of change by finding the difference in the y-coordinates divided by the difference in the x-coordinates.
Looking at function A:
Rate of change = (change in y) / (change in x) = (-1 - (-2)) / (4 - 0) = 1 / 4 = 0.25
Looking at function B:
Rate of change = (change in y) / (change in x) = (9 - 0) / (4 - 1) = 9 / 3 = 3
Looking at function C:
Rate of change = 1 (since y = x + 20 has a coefficient of 1 for x)
Based on the rate of change calculations, function B has the greatest rate of change.
2. The y-intercept of a function is the y-coordinate where the graph intersects the y-axis, which occurs when x = 0.
Looking at function A:
y-intercept = -2 since (0, -2) is a point on the graph.
Looking at function B:
y-intercept = 0 since (1, 0) is a point on the graph.
Looking at function C:
y-intercept = 20 since when x = 0, y = 20.
Based on the y-intercepts, function A has the smallest y-intercept.
3. To determine which function represents the money earned per hour, we need to consider the slope or rate of change. The higher the slope, the more money earned per hour.
Based on the earlier calculations, we found that function B has the greatest rate of change, indicating a higher slope. Therefore, function B would represent the money earned per hour more beneficially.
Matching the descriptions with the functions:
1. Function with the greatest rate of change: B
2. Function with the smallest y-intercept: A
3. Function that represents your money earned per hour the most: B
So the answers are:
1. Function with the greatest rate of change: B
2. Function with the smallest y-intercept: A
3. Function that would benefit you the most if it represented your money earned per hour: B