Let f(x) be a linear function with f(1) = 2 and f(3) = 8. Find f(5) .
Is the final answer 14 or 16
(1,2) and (3,8)
slope = 6/2 = 3
y = 3 x + b
2 = 3 + b
b = -1
so
y = 3 x - 1
if x = 5
y = 15 - 1
which is STILL 14 like Steve told you
If all else fails, make a table
x y
1 2
3 8
5 ?
Each time x changes by 2, y must change by the same amount for the graph to be a straight line.
So, since 8-2=6, 8+6=14
To find the value of f(5), we need to determine the equation of the linear function f(x) first.
Since f(x) is a linear function, it can be represented in the form f(x) = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we use the values of f(1) and f(3). Given that f(1) = 2 and f(3) = 8, we can set up the following equation:
f(3) - f(1) = (3 - 1)m
8 - 2 = 2m
6 = 2m
m = 6/2
m = 3
Now that we have the slope, we can find the y-intercept using one of the given points. Let's use the point (1, 2).
Using the equation f(x) = mx + b, we substitute the values of x = 1 and y = 2:
2 = 3(1) + b
2 = 3 + b
b = 2 - 3
b = -1
Therefore, the equation of the linear function f(x) is f(x) = 3x - 1.
Now, we can find f(5) by substituting x = 5 into the equation:
f(5) = 3(5) - 1
f(5) = 15 - 1
f(5) = 14
So the final answer is 14.