Which function produces a range of {-11,-5,1,7,13} given a domain of {-2,0,2,4,6}?
f(x)= −3x + 4
f(x)= −5x +3
f(x)= x + 2
f(x)= 3x -5
f(x)= x + 2
To determine which function produces the given range, we can substitute each value from the domain into each function and see which one leads to the desired range.
Let's try each function with the given domain:
1. f(x) = –3x + 4:
f(-2) = –3(-2) + 4 = 10
f(0) = –3(0) + 4 = 4
f(2) = –3(2) + 4 = –2
f(4) = –3(4) + 4 = –8
f(6) = –3(6) + 4 = –14
2. f(x) = –5x + 3:
f(-2) = –5(-2) + 3 = 13
f(0) = –5(0) + 3 = 3
f(2) = –5(2) + 3 = –7
f(4) = –5(4) + 3 = –17
f(6) = –5(6) + 3 = –27
3. f(x) = x + 2:
f(-2) = -2 + 2 = 0
f(0) = 0 + 2 = 2
f(2) = 2 + 2 = 4
f(4) = 4 + 2 = 6
f(6) = 6 + 2 = 8
4. f(x) = 3x - 5:
f(-2) = 3(-2) - 5 = -11
f(0) = 3(0) - 5 = -5
f(2) = 3(2) - 5 = 1
f(4) = 3(4) - 5 = 7
f(6) = 3(6) - 5 = 13
Among the four functions, only f(x) = 3x - 5 produces the desired range of {-11, -5, 1, 7, 13} for the given domain of {-2, 0, 2, 4, 6}.
To find which function produces the given range, we can substitute each value from the domain into each of the given functions and check which one produces the range {-11, -5, 1, 7, 13}.
Let's start by substituting the first value from the domain, -2, into each function:
1. f(x) = -3x + 4 ⇒ f(-2) = -3(-2) + 4 = 10
2. f(x) = -5x + 3 ⇒ f(-2) = -5(-2) + 3 = 13
3. f(x) = x + 2 ⇒ f(-2) = -2 + 2 = 0
4. f(x) = 3x - 5 ⇒ f(-2) = 3(-2) - 5 = -11
The first function, f(x) = -3x + 4, does not produce the range -11.
Now, let's substitute the second value from the domain, 0, into each function:
1. f(x) = -3x + 4 ⇒ f(0) = -3(0) + 4 = 4
2. f(x) = -5x + 3 ⇒ f(0) = -5(0) + 3 = 3
3. f(x) = x + 2 ⇒ f(0) = 0 + 2 = 2
4. f(x) = 3x - 5 ⇒ f(0) = 3(0) - 5 = -5
None of the functions produced the range -5.
Next, let's substitute the third value from the domain, 2, into each function:
1. f(x) = -3x + 4 ⇒ f(2) = -3(2) + 4 = -2
2. f(x) = -5x + 3 ⇒ f(2) = -5(2) + 3 = -7
3. f(x) = x + 2 ⇒ f(2) = 2 + 2 = 4
4. f(x) = 3x - 5 ⇒ f(2) = 3(2) - 5 = 1
The third function, f(x) = x + 2, does not produce the range -11, -5, or 7.
Now, let's substitute the fourth value from the domain, 4, into each function:
1. f(x) = -3x + 4 ⇒ f(4) = -3(4) + 4 = -8
2. f(x) = -5x + 3 ⇒ f(4) = -5(4) + 3 = -17
3. f(x) = x + 2 ⇒ f(4) = 4 + 2 = 6
4. f(x) = 3x - 5 ⇒ f(4) = 3(4) - 5 = 7
The fourth function, f(x) = 3x - 5, produces the range 7, which matches one of the given values.
Finally, let's substitute the last value from the domain, 6, into each function:
1. f(x) = -3x + 4 ⇒ f(6) = -3(6) + 4 = -14
2. f(x) = -5x + 3 ⇒ f(6) = -5(6) + 3 = -27
3. f(x) = x + 2 ⇒ f(6) = 6 + 2 = 8
4. f(x) = 3x - 5 ⇒ f(6) = 3(6) - 5 = 13
The fourth function, f(x) = 3x - 5, also produces the range 13, which matches the last given value.
Therefore, the function f(x) = 3x - 5 produces the given range {-11, -5, 1, 7, 13} given the domain {-2, 0, 2, 4, 6}.