What is the range of y = -3x + 1 for the domain of {2,8)?
A. 8
B. 2
C. -23
D. -5
The Correct Answer and Explanation is:
To find the range of the function ( y = -3x + 1 ) for the domain ( {2, 8} ), we need to calculate the corresponding ( y )-values for each ( x )-value in the domain and then determine the range.
Step 1: Understanding the function
The given function is ( y = -3x + 1 ), which is a linear function. This means that for each value of ( x ), we can substitute it into the equation to find the corresponding value of ( y ).
Step 2: Substituting the values from the domain
The domain is ( {2, 8} ), meaning we need to find the ( y )-values when ( x = 2 ) and ( x = 8 ).
- When ( x = 2 ):
[
y = -3(2) + 1 = -6 + 1 = -5
]
So, when ( x = 2 ), ( y = -5 ). - When ( x = 8 ):
[
y = -3(8) + 1 = -24 + 1 = -23
]
So, when ( x = 8 ), ( y = -23 ).
Step 3: Determining the range
The range of a function is the set of all possible values of ( y ) corresponding to the values of ( x ) in the domain. From the calculations above, we found that for the domain ( {2, 8} ), the corresponding ( y )-values are:
- ( y = -5 ) when ( x = 2 )
- ( y = -23 ) when ( x = 8 )
Thus, the range of the function for the domain ( {2, 8} ) is the set of ( y )-values ( {-5, -23} ).
Step 4: Identifying the correct answer
From the options provided:
- A. 8
- B. 2
- C. -23
- D. -5
We can see that none of these options directly represent the full range (which is ( {-5, -23} )), but since the range includes the value ( -5 ), the correct answer from the given choices is D. -5.