To determine which equation matches the given table, we start by analyzing the equations provided. The two equations are:
- y = x3
- y = 4x3
The first equation, y = x3, describes a cubic function where the output (y) is equal to the cube of the input (x). In this case, each value of x will be raised to the power of 3.
The second equation, y = 4x3, also describes a cubic function but with a vertical stretch factor of 4. This means that for every x-value, the corresponding y-value will be four times greater than it would be in the equation y = x3.
To find out which equation matches the given table, let’s assume we have a set of values for x and calculate the corresponding y values for both equations:
- For x = 1:
- y = 13 = 1
- y = 4(13) = 4(1) = 4
- For x = 2:
- y = 23 = 8
- y = 4(23) = 4(8) = 32
By comparing values, we can see that for x = 1, y matches the output of the first equation, and for x = 2, y matches the output of the second equation if that value is in the table.
Hence, when considering the full context of the table, we can match each point to determine which equation is applicable. The equation that corresponds to the values in the table will either be y = x3 or y = 4x3 based on the output values shown.