How are the functions y = x and y = x – 3 related? How are their graphs related?
(1 point)
Responses
Each output for y = x – 3 is 3 more than the corresponding output for y = x.
The graph of y = x – 3 is the graph of y = x translated down 3 units.
Each output for y = x – 3 is 3 more than the corresponding output for y = x . The graph of y = x – 3 is the graph of y = x translated down 3 units.
Each output for y = x – 3 is 3 more than the corresponding output for y = x.
The graph of y = x – 3 is the graph of y = x translated up 3 units.
Each output for y = x – 3 is 3 more than the corresponding output for y = x . The graph of y = x – 3 is the graph of y = x translated up 3 units.
Each output for y = x – 3 is 3 less than the corresponding output for y = x.
The graph of y = x – 3 is the graph of y = x translated down 3 units.
Each output for y = x – 3 is 3 less than the corresponding output for y = x . The graph of y = x – 3 is the graph of y = x translated down 3 units.
Each output for y = x – 3 is 3 less than the corresponding output for y = x.
The graph of y = x – 3 is the graph of y = x translated up 3 units.
Each output for y = x – 3 is 3 less than the corresponding output for y = x . The graph of y = x – 3 is the graph of y = x translated up 3 units.
Each output for y = x – 3 is 3 less than the corresponding output for y = x.
The graph of y = x – 3 is the graph of y = x translated down 3 units.
Each output for y = x – 3 is 3 less than the corresponding output for y = x. The graph of y = x – 3 is the graph of y = x translated down 3 units.
Each output for y = x – 3 is 3 less than the corresponding output for y = x. This means that if you take any value of x, subtract 3, and plug it into y = x – 3, you will get a result that is 3 less than the result you would get by plugging the same x value into y = x.
The graph of y = x – 3 is the graph of y = x translated down 3 units. This means that the graph of y = x – 3 is identical to the graph of y = x, but shifted downwards by 3 units. Every point on the graph of y = x – 3 will be 3 units below the corresponding point on the graph of y = x.
To see this relationship, you can make a table of values for both functions and compare the results. For example, if you choose x = 0, y = x – 3 gives you y = -3, which is 3 less than the y value of y = x when x = 0. Similarly, if you choose x = 1, y = x – 3 gives you y = -2, which is also 3 less than the y value of y = x when x = 1. You can continue to compare the values for different x values to see that they are always 3 less when using y = x – 3.
To graph the functions, you can plot points using the values from the tables or use the slope-intercept form to find the y-intercepts and slopes. The graph of y = x – 3 will be a straight line that is parallel to the graph of y = x, but shifted 3 units downward.