graphing linear equations review unit 3 lesson 11
match the description with the correct function
function a (0,-2) (4,-1) (8,0)
function b:
x 0 4 8
y 1 9 17
function c: y=x+20
function with the greatest rate of change _
function with the smallest y-intercept _
which function would benefit you the most if represented your money earned per hour? _
function with the highest initial amount of money __
function a function b function c
function with the greatest rate of change: function c.
function with the smallest y-intercept: function a.
which function would benefit you the most if represented your money earned per hour? function c.
function with the highest initial amount of money: function b.
Function with the greatest rate of change: function b (x 0 4 8, y 1 9 17). This function has a constant rate of change of 8.
Function with the smallest y-intercept: function a (0,-2) (4,-1) (8,0). This function has a y-intercept of -2.
Function that would benefit you the most if represented your money earned per hour: function c (y = x + 20). This function represents a linear relationship where the y-value (money earned per hour) increases by 1 unit for every 1 unit increase in the x-value (hours worked). Therefore, this function would represent the highest earnings per hour.
Function with the highest initial amount of money: function a (0,-2) (4,-1) (8,0). This function has an initial amount of money of -2.
Summary:
- Function with the greatest rate of change: b
- Function with the smallest y-intercept: a
- Function that would benefit you the most if represented your money earned per hour: c
- Function with the highest initial amount of money: a
To match the descriptions with the correct function, let's analyze the given functions.
Function a: (0,-2) (4,-1) (8,0)
This function is represented by a set of points. Each point consists of an x-coordinate and a corresponding y-coordinate. The three given points are (0,-2), (4,-1), and (8,0).
Function b: x 0 4 8, y 1 9 17
This function is represented by two separate lists of numbers. The first list corresponds to the x-values, which are 0, 4, and 8. The second list corresponds to the y-values, which are 1, 9, and 17.
Function c: y = x + 20
This function is represented by an equation in the form y = mx + b. In this case, the coefficient of x is 1, and the y-intercept (the value of y when x = 0) is 20.
Now, let's match the descriptions with the correct function:
- Function with the greatest rate of change:
To determine the rate of change for each function, we need to calculate the slope. The slope is determined by subtracting the y-values and dividing by the difference in x-values.
Function a: Slope = (0 - (-2)) / (4 - 0) = 2 / 4 = 0.5
Function b: Slope = (9 - 1) / (4 - 0) = 8 / 4 = 2
Function c: Since function c is in the form y = x + 20, the coefficient of x (which represents the slope) is 1. Therefore, the slope of function c is 1.
Function b has the greatest rate of change because it has the highest slope.
- Function with the smallest y-intercept:
The y-intercept is the value of y when x = 0.
Function a: y-intercept = -2
Function b: y-intercept = 1
Function c: y-intercept = 20
Function a has the smallest y-intercept because it has a value of -2.
- Function that would benefit you the most if represented your money earned per hour:
Based on the given information, we can determine that the function representing money earned per hour would be the one where x represents the number of hours worked, and y represents the amount of money earned.
Function a and function b have sets of ordered pairs, so they are not suitable for this purpose.
Function c, y = x + 20, represents the amount of money earned per hour because the coefficient of x (m) represents the money earned per hour, and the y-intercept (b) represents the initial amount of money earned even if no hours are worked.
Therefore, function c would benefit you the most if it represented your money earned per hour.
- Function with the highest initial amount of money:
The initial amount of money is represented by the y-intercept.
Considering the y-intercepts from earlier:
Function a: Initial amount of money = -2
Function b: Initial amount of money = 1
Function c: Initial amount of money = 20
Function c has the highest initial amount of money because it has a value of 20.
Matching the descriptions with the correct function:
- Function with the greatest rate of change: Function b
- Function with the smallest y-intercept: Function a
- Function that would benefit you the most if represented your money earned per hour: Function c
- Function with the highest initial amount of money: Function c
function c has the highest initial amount of money
Apologies for the confusion. You are right, function c has the highest initial amount of money. Thank you for catching that mistake.
The correct matching is:
- Function with the greatest rate of change: Function b
- Function with the smallest y-intercept: Function a
- Function that would benefit you the most if represented your money earned per hour: Function c
- Function with the highest initial amount of money: Function c