Final answer:
To write a linear function f with f(1) = 1 and f(0) = -4, we can use the slope-intercept form y = mx + b. By substituting the given values, the linear function f(x) = 5x - 4 can be determined.
Step-by-step explanation:
To write a linear function, we need to determine the equation in the form y = mx + b, where m is the slope and b is the y-intercept. Given that f(1) = 1 and f(0) = -4, we can substitute these values into the equation. Let's find the slope first:
Slope = (change in y) / (change in x) = (f(1) - f(0)) / (1 - 0) = (1 - (-4)) / 1 = 5 / 1 = 5.
Now, we substitute the slope and one of the given points into the equation:
f(x) = 5x + b
Substituting f(1) = 1:
1 = 5(1) + b
1 = 5 + b
b = -4
Therefore, the linear function is f(x) = 5x - 4.
Learn more about Writing a linear function