Finding the Range of the Function y = 2x + 3
To determine the range of the function y = 2x + 3 given the domain {0, 2, 6}, we will evaluate the function at each value of x in the specified domain.
Step 1: Evaluate y at x = 0
When x = 0:
y = 2(0) + 3 = 3
Thus, y = 3.
Step 2: Evaluate y at x = 2
When x = 2:
y = 2(2) + 3 = 4 + 3 = 7
Thus, y = 7.
Step 3: Evaluate y at x = 6
When x = 6:
y = 2(6) + 3 = 12 + 3 = 15
Thus, y = 15.
Step 4: Compile the Results
The computed values of y for the specified domain are:
- y(0) = 3
- y(2) = 7
- y(6) = 15
Conclusion: The Range
Therefore, the range of the function y = 2x + 3 for the given domain of {0, 2, 6} is:
{3, 7, 15}