find the range of the function defined by the equation and the given domain.
f(x)=3/x-6; D={-3,0,3,9}
The range can be found by plugging the values of the domain in the equation. For example, 3/(-3-6)=-1/3
-1/3 is part of the range because the range represents the outputs or y values that correspond to the inputs (the domain), or x values
To find the range of the function f(x) = 3/(x - 6) with the given domain D = {-3, 0, 3, 9}, we need to evaluate the function for each value in the domain and determine the corresponding range.
Let's substitute each value from the domain into the function and simplify:
For x = -3:
f(-3) = 3/(-3 - 6) = 3/(-9) = -1/3
For x = 0:
f(0) = 3/(0 - 6) = 3/(-6) = -1/2
For x = 3:
f(3) = 3/(3 - 6) = 3/(-3) = -1
For x = 9:
f(9) = 3/(9 - 6) = 3/3 = 1
The range of the function f(x) = 3/(x - 6) with the given domain D = {-3, 0, 3, 9} is {-1/3, -1/2, -1, 1}.
To find the range of the function defined by the equation f(x) = 3/(x - 6) with a given domain D = {-3, 0, 3, 9}, we need to determine the set of possible output values or y-values.
1. Start by determining the possible output values for each x-value in the domain. Substitute each value from the domain into the equation f(x) = 3/(x - 6) to find the corresponding y-value.
- For x = -3: f(-3) = 3/(-3 - 6) = 3/(-9) = -1/3
- For x = 0: f(0) = 3/(0 - 6) = 3/(-6) = -1/2
- For x = 3: f(3) = 3/(3 - 6) = 3/(-3) = -1
- For x = 9: f(9) = 3/(9 - 6) = 3/3 = 1
2. Now, collect all the possible y-values obtained in Step 1 to determine the range of the function.
- Range = {-1/3, -1/2, -1, 1}
Thus, the range of the function f(x) = 3/(x - 6) with a domain D = {-3, 0, 3, 9} is {-1/3, -1/2, -1, 1}.