Question

Which function produces a range of {−11,−5,1,4,10} given a domain of {−2,0,1,3,5}?
f(x) = −2x − 5
f(x) = x + 2
f(x) = −3x + 4
f(x) = −5x + 3

Answer 1

To determine which function produces the given range, we can substitute each value from the domain into each of the functions and see which one yields the desired range.

1. f(x) = −2x − 5
f(-2) = -2(-2) - 5 = 4 - 5 = -1
f(0) = -2(0) - 5 = 0 - 5 = -5
f(1) = -2(1) - 5 = -2 - 5 = -7
f(3) = -2(3) - 5 = -6 - 5 = -11
f(5) = -2(5) - 5 = -10 - 5 = -15

2. f(x) = x + 2
f(-2) = -2 + 2 = 0
f(0) = 0 + 2 = 2
f(1) = 1 + 2 = 3
f(3) = 3 + 2 = 5
f(5) = 5 + 2 = 7

3. f(x) = −3x + 4
f(-2) = -3(-2) + 4 = 6 + 4 = 10
f(0) = -3(0) + 4 = 0 + 4 = 4
f(1) = -3(1) + 4 = -3 + 4 = 1
f(3) = -3(3) + 4 = -9 + 4 = -5
f(5) = -3(5) + 4 = -15 + 4 = -11

4. f(x) = −5x + 3
f(-2) = -5(-2) + 3 = 10 + 3 = 13
f(0) = -5(0) + 3 = 0 + 3 = 3
f(1) = -5(1) + 3 = -5 + 3 = -2
f(3) = -5(3) + 3 = -15 + 3 = -12
f(5) = -5(5) + 3 = -25 + 3 = -22

Based on the results, only the function f(x) = −3x + 4 produces the desired range of {-11, -5, 1, 4, 10} given the domain of {-2, 0, 1, 3, 5}.