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What kind of transformation would add 4 to the x-values of every point in a shape and subtract 2 from the y values of every point in a shape?
The transformation from y = f(x) to y = f(x - 4) - 2
What is the change in x values on a given line?
The change in x values on a given line refers to the difference between the x-coordinates of two points on that line. It is calculated by subtracting the initial x value from the final x value, expressed as Δx = x₂ - x₁. This change can help determine the slope of the line, as the slope is the ratio of the change in y values (Δy) to the change in x values (Δx). Understanding this change is essential in analyzing the line's behavior and direction.
Does a transformation ever change the shape of a figure?
Yes. The transformation from y = f(x) to y=f(2x) will compress the shape along the x-axis by a factor of 2.
What is the scientific definition of slope?
Change in y values over change in x values. Rise over run.
How do your rotate a figure 90 degrees clockwise?
To rotate a figure 90 degrees clockwise around a point, take each point of the figure and apply the following transformation: if the original point is at coordinates (x, y), the new coordinates after rotation will be (y, -x). This means you swap the x and y values and change the sign of the new x value. Make sure to apply this transformation to each point of the figure to get the complete rotated image.
What kind of transformation would add 4 to the x-values of every point in a shape and subtract 2 from the y values of every point in a shape?
The transformation from y = f(x) to y = f(x - 4) - 2
What is the change in x values on a given line?
The change in x values on a given line refers to the difference between the x-coordinates of two points on that line. It is calculated by subtracting the initial x value from the final x value, expressed as Δx = x₂ - x₁. This change can help determine the slope of the line, as the slope is the ratio of the change in y values (Δy) to the change in x values (Δx). Understanding this change is essential in analyzing the line's behavior and direction.
What is one advantage of transforming X values into z scores?
The transformation always creates a normal shaped distribution.
Does a transformation ever change the shape of a figure?
Yes. The transformation from y = f(x) to y=f(2x) will compress the shape along the x-axis by a factor of 2.
What is the scientific definition of slope?
Change in y values over change in x values. Rise over run.
Why do linear functions have a rate of change?
Linear functions have a rate of change because their slope parameter is non-zero. That is, as their x or y values changes, their corresponding x or y values change in response.
Constants are variables that can'ts or can change?
Constant : these refers to values which do not change. they have the same value throughout the process. Like "1" is a constant value it will never change 1 will always remain 1. i.e.1=1 Varaibles= these refers to those quantities or values which change.for eg. if in a mathematical equation we have "X" variable. Now "X" can have number of values X =2 or X= 3 or X=10000 so they are called variables because their values change.
In an inverse relationship how do the values of y change as the values of x increase?
Y would decrease in value as X increases in value.
In an inverse relationship how do the values of y change as the values of x is decreased?
The value of y increases, such that x*y remains a constant.
What is the benefit of always writing slope as a function?
This will emphasize the 'rise over run' expression of slope. In other words, the change in y over the change in x. This show the run, or change in x values, even if the slope is a whole number. A slope of 3 becomes 3/1 showing the change in y-values to be 3 and the change in x-values to be 1.
How can you calculate the slope from a table?
To calculate the slope from a table, identify two points represented in the table, typically given as (x₁, y₁) and (x₂, y₂). Use the formula for slope, which is (y₂ - y₁) / (x₂ - x₁). This gives you the change in the y-values divided by the change in the x-values, indicating how much y changes for a one-unit change in x. Ensure the x-values are not the same to avoid division by zero.
How do you calculate an average in a graph?
change in y values of 1st and last points divided by the change in x values of the 1st and last points
