Quadrant Transformations Quiz | Math Scatter Plot Review

In Quadrant 2, the transformations that are applicable are y squared, reciprocal x, and log x. When a function is squared, it reflects across the x-axis, resulting in a positive y-value. The reciprocal of x reflects the function across the y-axis, while the logarithm of x reflects it across the y-axis as well, but with a different rate of change. These transformations help to understand the behavior of the function in Quadrant 2.

In Quadrant 3, the x-coordinate is negative while the y-coordinate is positive. The reciprocal of a negative number is also negative, so the transformation of reciprocal x is applicable in Quadrant 3. Similarly, the reciprocal of a positive number is positive, so the transformation of reciprocal y is applicable in Quadrant 3. Additionally, logarithmic functions are defined for positive numbers, so the transformations of log x and log y are also applicable in Quadrant 3.

In Quadrant 4, the x-values are positive and the y-values are negative. Therefore, the transformations that are applicable in this quadrant are x squared (which keeps the x-values positive), reciprocal y (which changes the sign of the y-values), and log y (which is only defined for negative y-values).

The appropriate quadrants for an x squared transformation are Quadrant 1 and Quadrant 4. In Quadrant 1, both the x and y coordinates are positive, and when x is squared, the resulting y value will also be positive. In Quadrant 4, the x coordinate is positive and the y coordinate is negative, and when x is squared, the resulting y value will still be positive. Therefore, the x squared transformation is appropriate for these two quadrants.

A y squared transformation refers to a transformation in which the y-coordinate of a point is squared. In this transformation, the sign of the y-coordinate does not change, but its value is squared. Since squaring a positive number results in a positive number, Quadrant 1 and Quadrant 2 are appropriate for a y squared transformation. In these quadrants, the y-coordinates are positive, and squaring them will still yield positive values. Quadrant 3 and Quadrant 4, on the other hand, have negative y-coordinates, and squaring them will result in positive values, which is not appropriate for a y squared transformation.

A log x transformation is appropriate for Quadrant 2 and Quadrant 3. In Quadrant 2, the x-values are negative and the y-values are positive, while in Quadrant 3, both the x-values and y-values are negative. A log x transformation is used to transform skewed data with positive and negative values into a more symmetrical distribution. Therefore, Quadrant 2 and Quadrant 3 are appropriate for a log x transformation.

A log y transformation is appropriate for Quadrant 3 and Quadrant 4. This is because in these quadrants, the y-values are negative or zero, which cannot be directly plotted on a logarithmic scale. By applying a log y transformation, the negative or zero values can be transformed into positive values, allowing them to be plotted on a logarithmic scale. Quadrant 1 and Quadrant 2 have positive y-values, which can be directly plotted on a logarithmic scale without the need for a transformation.

A 1/y transformation involves taking the reciprocal of the y-coordinate of a point. When we take the reciprocal of a positive y-coordinate, the resulting value will be positive. Therefore, points in Quadrant 1 and Quadrant 2, where the y-coordinates are positive, are not appropriate for a 1/y transformation. However, in Quadrant 3 and Quadrant 4, where the y-coordinates are negative, taking the reciprocal will result in positive values. Hence, Quadrant 3 and Quadrant 4 are appropriate for a 1/y transformation.

A 1/x transformation is appropriate for Quadrant 2 and Quadrant 3. In Quadrant 2, the x-values are positive while the y-values are negative, which allows for the transformation to be applied. In Quadrant 3, both the x-values and y-values are negative, also allowing for the transformation. In Quadrant 1, both x-values and y-values are positive, which does not fit the criteria for a 1/x transformation. In Quadrant 4, the x-values are negative while the y-values are positive, which also does not fit the criteria.

Transformations in Quadrant 1 refer to the changes in the coordinates of a point in the Cartesian plane when it is subjected to certain operations. In this case, the effect of these transformations is to stretch both the x and y values. This means that the x and y coordinates of a point will be multiplied by a factor greater than 1, resulting in a larger distance from the origin in both the horizontal and vertical directions. This stretching effect is characteristic of transformations in Quadrant 1.

Transformations in Quadrant 2 refer to changes made to the coordinates of points in the second quadrant of a coordinate plane. In this quadrant, the x values are negative and the y values are positive. The given answer states that transformations in Quadrant 2 stretch the y values and compress the x values. This means that the y values of the points will be multiplied by a factor greater than 1, causing them to increase in magnitude, while the x values will be multiplied by a factor between 0 and 1, causing them to decrease in magnitude.

Transformations in Quadrant 3 refer to the region of the coordinate plane where both the x and y values are negative. In this quadrant, the x values and y values are compressed, meaning they are scaled down or reduced in size. This can be visualized as a shrinking or narrowing effect on the coordinate points in Quadrant 3. Therefore, the correct answer is that transformations in Quadrant 3 compress both the x values and y values.

Transformations in Quadrant 4 have the effect of stretching x values and compressing y values. This means that the x-coordinates of the points in the graph will be stretched horizontally, making the graph wider. On the other hand, the y-coordinates of the points will be compressed vertically, making the graph shorter. This can be visualized as a horizontal stretching and vertical compression of the graph in Quadrant 4.

The scatter plot above is appropriate for Quadrant 4 because it shows a positive relationship between the variables. In Quadrant 4, both the x-axis and y-axis values are positive, indicating that as one variable increases, the other variable also increases. This positive correlation is reflected in the scatter plot, where the points are clustered in the upper right quadrant.

The scatter plot above is appropriate for Quadrant 2 because it shows a negative correlation between the two variables. In this quadrant, the x-values are negative while the y-values are positive. This indicates that as the x-values decrease, the y-values increase. Therefore, the scatter plot fits in Quadrant 2.

The scatter plot above is appropriate for Quadrant 3 because all the data points are located in the lower left region of the plot. In Quadrant 3, the x-coordinates are negative and the y-coordinates are also negative. This indicates a negative relationship between the variables being plotted, with both variables decreasing as the values increase.

Since the answer is "None of these," it means that none of the quadrants (Quadrant 1, Quadrant 2, Quadrant 3, or Quadrant 4) is an appropriate shape for the scatter plot above. This suggests that the scatter plot does not exhibit a clear pattern or relationship between the variables being plotted.

Since the question does not provide any information about the scatter plot or its data, it is not possible to determine which quadrant is appropriate for the scatter plot. Therefore, the correct answer is "None of these".

The transformations that are applicable in Quadrant 1 are x squared and y squared. This means that the values of x and y are squared, resulting in a positive value for both x and y. The reciprocal transformations (reciprocal x and reciprocal y) would not be applicable in Quadrant 1 because they would result in negative values for x or y. Similarly, the logarithmic transformations (log x and log y) would also not be applicable in Quadrant 1 as they would result in undefined or negative values for x or y.

The scatter plot above is appropriate for Quadrant 1 because all the data points are located in the positive x-axis and positive y-axis. In Quadrant 1, both the x and y values are positive, indicating a positive relationship between the variables being plotted.