The equation y=3x-2 has range values of 1, 7, 13, 16, 19 Which number is in the domain of the function?
SHOW WORK
To find the domain of the function, we need to solve for x. We can rearrange the equation as:
x = (y + 2)/3
Now we can plug in the given values for y and solve for x:
- When y = 1, x = (1 + 2)/3 = 1
- When y = 7, x = (7 + 2)/3 = 3
- When y = 13, x = (13 + 2)/3 = 5
- When y = 16, x = (16 + 2)/3 = 6
- When y = 19, x = (19 + 2)/3 = 7
The values of x we found are 1, 3, 5, 6, and 7. Therefore, the domain of the function includes the numbers 1, 3, 5, 6, and 7.
To determine which number is in the domain of the function, we need to find the corresponding x-values for the given range values.
Given equation: y = 3x - 2
For the range value 1:
1 = 3x - 2
3x = 1 + 2
3x = 3
x = 3/3
x = 1
For the range value 7:
7 = 3x - 2
3x = 7 + 2
3x = 9
x = 9/3
x = 3
For the range value 13:
13 = 3x - 2
3x = 13 + 2
3x = 15
x = 15/3
x = 5
For the range value 16:
16 = 3x - 2
3x = 16 + 2
3x = 18
x = 18/3
x = 6
For the range value 19:
19 = 3x - 2
3x = 19 + 2
3x = 21
x = 21/3
x = 7
Therefore, the numbers that correspond to the given range values and are in the domain of the function are: 1, 3, 5, 6, 7.