The table represents some points on the graph of linear function `f.`
x:-3,2,5,11
f(x):-130,0,78,234
Which function represents `f?`
f\left(x\right)=26\left(x-2\right)
f\left(x\right)=-26\left(2x-1\right)
f\left(x\right)\ =13\left(x-2\right)
f\left(x\right)=-2\left(26x-1\right)
To determine which function represents `f`, we can plug in the given points (-3, -130), (2, 0), (5, 78), and (11, 234) into each of the functions and see which one matches the given points.
Let's test each function with the given points:
1. f(x) = 26(x-2)
For x = -3: f(-3) = 26(-3-2) = 26(-5) = -130 ✓
For x = 2: f(2) = 26(2-2) = 26(0) = 0 ✓
For x = 5: f(5) = 26(5-2) = 26(3) = 78 ✓
For x = 11: f(11) = 26(11-2) = 26(9) = 234 ✓
2. f(x) = -26(2x-1)
For x = -3: f(-3) = -26(2(-3)-1) = -26(-7) = 182 ❌
For x = 2: f(2) = -26(2(2)-1) = -26(3) = -78 ❌
For x = 5: f(5) = -26(2(5)-1) = -26(9) = -234 ❌
For x = 11: f(11) = -26(2(11)-1) = -26(21) = -546 ❌
3. f(x) = 13(x-2)
For x = -3: f(-3) = 13(-3-2) = 13(-5) = -65 ❌
For x = 2: f(2) = 13(2-2) = 13(0) = 0 ✓
For x = 5: f(5) = 13(5-2) = 13(3) = 39 ❌
For x = 11: f(11) = 13(11-2) = 13(9) = 117 ❌
4. f(x) = -2(26x-1)
For x = -3: f(-3) = -2(26(-3)-1) = -2(-79) = 158 ❌
For x = 2: f(2) = -2(26(2)-1) = -2(52) = -104 ❌
For x = 5: f(5) = -2(26(5)-1) = -2(129) = -258 ❌
For x = 11: f(11) = -2(26(11)-1) = -2(285) = -570 ❌
Based on the tests, the function that represents `f` is f(x) = 26(x-2).