Determine which function has the greater rate of change in problems 1-3
1. y = x + 3; y = x + 5
The rate of change is the same for both functions.
2. y = 2x + 3; y = 3x + 3
The function y = 3x + 3 has the greater rate of change.
3. y = 4x + 2; y = 2x + 4
The function y = 4x + 2 has the greater rate of change.
To determine which function has the greater rate of change in problems 1-3, we need to calculate the rate of change for each function in each problem.
The rate of change of a function represents how much the value of the function's output changes for every unit increase in the input variable.
Here are the steps to calculate the rate of change for each function in each problem:
1. Select Problem 1 and the two functions given in that problem.
2. Choose two different input values (x1 and x2) for Problem 1. These values should be numerical and distinct.
3. Plug the first input value (x1) into each function separately and calculate the corresponding output values (y1) for each function.
4. Repeat step 3 with the second input value (x2) for each function, obtaining the corresponding output values (y2) for each function.
5. Calculate the rate of change for each function by using the formula: rate of change = (y2 - y1) / (x2 - x1).
6. Repeat steps 2-5 for Problem 2 and Problem 3, using the functions given in each respective problem.
Once you have calculated the rate of change for each function in each problem, compare the results to determine which function has the greater rate of change in problems 1-3. The function with the larger rate of change indicates that its output value changes at a faster rate compared to the other function.
To determine which function has the greater rate of change in problems 1-3, we need to find the rate of change for each function. The rate of change is calculated by finding the slope of the function.
1. Find the slope of function 1: The slope of a linear function can be found by dividing the change in y-coordinates by the change in x-coordinates between two points on the line. For example, if function 1 is represented by the equation y = mx + b, where m is the slope, then the rate of change is m.
2. Find the slope of function 2: Similarly, find the slope of function 2 by dividing the change in y-coordinates by the change in x-coordinates between two points on the line. If function 2 is represented by the equation y = nx + c, where n is the slope, then the rate of change is n.
3. Compare the slopes: Compare the slopes of function 1 and function 2. The function with the greater slope or rate of change will have a steeper line or a greater increase or decrease in y-values for a given change in x-values.
After comparing the slopes or rates of change for each function, you can determine which one has the greater rate of change in problems 1-3.