How is the function shown below related to yx? Graph the function by translating the parent function.
y=x-4
The function y = x - 4 is a linear function that is related to the parent function y = x by a translation.
The parent function y = x is a straight line with a slope of 1 and passes through the origin (0,0).
By subtracting 4 from the x-values, the translated function y = x - 4 shifts the graph of the parent function downward by 4 units.
To graph the function y = x - 4, start with the points on the parent function y = x and then shift them downward by 4 units.
For example, when x = 0, the parent function has a y-value of 0. However, for the translated function y = x - 4, when x = 0, the corresponding y-value is -4.
By connecting all the translated points, you will get a straight line that is parallel to the parent function but shifted downward by 4 units.
The function y = x - 4 is related to y = x through a translation. Specifically, the function y = x - 4 shifts the parent function y = x downward by 4 units. This means that for every x-value, the corresponding y-value will be 4 units smaller.
To graph the function by translating the parent function, you can follow these steps:
1. Start by plotting a few points on the parent function y = x. For example, you can choose x-values like -2, -1, 0, 1, and 2.
For each x-value, calculate the corresponding y-value by substituting the x-value into the equation y = x. For example, when x = -2, y = -2; when x = -1, y = -1; when x = 0, y = 0; when x = 1, y = 1; and when x = 2, y = 2.
2. Once you have the points plotted for the parent function y = x, shift each point downward by 4 units to represent the translated function y = x - 4. For example, when x = -2, y = -2 - 4 = -6; when x = -1, y = -1 - 4 = -5; when x = 0, y = 0 - 4 = -4; when x = 1, y = 1 - 4 = -3; and when x = 2, y = 2 - 4 = -2.
3. Connect the points to create a smooth line. This line represents the graph of the translated function y = x - 4.
By following these steps, you can graph the function y = x - 4 by translating the parent function y = x downward by 4 units.
The function y = x - 4 is a linear function. It is related to yx in the sense that it represents a translation of the parent function y = x by moving it 4 units down along the y-axis.
To graph this function, you can start by plotting some points and then connecting them to form a straight line. Here's how you can do it:
1. Choose a range of values for x. For example, let's say x ranges from -5 to 5.
2. Substitute each value of x into the equation y = x - 4 to find the corresponding y-values. For instance, when x = -5, y = -5 - 4 = -9. Similarly, when x = 0, y = 0 - 4 = -4, and so on.
3. Plot the points (x, y) that you found in the previous step on a graph.
4. Connect the points with a straight line. Since the function is linear, you can assume that the line extends infinitely in both directions.
The resulting graph will be a straight line with a slope of 1 (because the coefficient of x is 1) and a y-intercept of -4 (because when x = 0, y = -4). The line will be translated 4 units down from the parent function y = x.