Find the range of the function for the given domain. π(π₯) = 3π₯ β 8;{β2, β1, 0, 1, 2} no mater what I do I cant find the answer.
The domain of a function consists of your choice of x values that you can use.
The range would be the set of values that are the result of using the domain values.
e.g.
if x = -2 , f(-2) = 3(-2) - 8 = -14
if x = -1 , f(-1) = 3(-1) - 8 = -11
...(x) '
if x = 2 , f(2) = 3(2) - 8 = -2
So the range would be the set of numbers from the f(x)s above.
To find the range of a function, you need to substitute the values from the given domain into the function and see what outputs you get. Let's calculate the values of the function π(π₯) = 3π₯ β 8 for each value in the domain {β2, β1, 0, 1, 2}.
For π₯ = -2:
π(π₯) = 3(β2) β 8
= -6 - 8
= -14
For π₯ = -1:
π(π₯) = 3(β1) β 8
= -3 - 8
= -11
For π₯ = 0:
π(π₯) = 3(0) β 8
= 0 - 8
= -8
For π₯ = 1:
π(π₯) = 3(1) β 8
= 3 - 8
= -5
For π₯ = 2:
π(π₯) = 3(2) β 8
= 6 - 8
= -2
Now, look at the outputs we obtained: -14, -11, -8, -5, -2. The range of the function π(π₯) = 3π₯ β 8 is the set of all these output values, which is {-14, -11, -8, -5, -2}. Thus, the range of the function for the given domain is {-14, -11, -8, -5, -2}.