Linear Parent Function
x →∞, f(x) →∞x → -∞, f(x) → ∞
The linear parent function is a function of the form f(x) = mx + b, where m and b are constants. This function is called a parent function because it is the simplest form of a straight line graph, from which all other linear functions can be derived with certain transformations.
The variable x represents the independent variable, while f(x) represents the dependent variable. The constant m is the slope of the line, and it determines the steepness of the line, while the constant b is the y-intercept, which is the point where the line intersects the y-axis.
When graphing a linear function, it’s important to note that the slope determines the direction of the line. If m > 0, then the line is increasing from left to right, while if m < 0, then the line is decreasing from left to right. The y-intercept, or the point where the line crosses the y-axis, can be found by setting x = 0 and solving for y. In general, linear functions are used to model relationships between two variables that have a constant rate of change. They also have a wide range of applications, including in economics, physics, and engineering.
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