By using the piecewise function, the output value of f(3) include the following; f(3) = -6.25.
In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:
Where:
- x and y represent the data points.
- m represent the slope.
First of all, we would determine the slope of this upward sloping line by using the rise and run;
Slope (m) = rise/run
Slope (m) = -3/4.
At data point (0, -4) and a slope of -3/4, a function for this line can be calculated by using the point-slope form as follows:
y + 4 = -3/4(x - 0)
y = -3/4(x) - 4
f(x) = -3/4(x) - 4, when 1 < x < 4
When x is 3, the value of f(x) is given by;
f(3) = -3/4(3) - 4
f(3) = -6.25