In the equation f(t) = 4t + 9, which of the following is the independent variable?
The independent variable in the equation f(t) = 4t + 9 is t.
In function notation, the input value, often represented as t, is the independent variable. The function's output, or the dependent variable, depends on the value of the independent variable.
f is not the independent variable in this equation. Instead, it represents the function itself, or more specifically, the value of the function f at a particular input t. The output f(t) depends on the value of the input t, making f the dependent variable in this equation.
t is the independent variable in this equation. It represents the input into the function f. The value of f(t) changes based on the value of t. Therefore, t is the independent variable, as its value can be freely chosen and does not depend on any other variable in the equation.
4 is not an independent variable but a coefficient of the independent variable t in the equation. It indicates the rate at which the value of f(t) changes for each unit change in t. It is a constant that does not change.
9 is a constant term in the equation and not a variable. It represents the value of f(t) when the value of t is zero (the y-intercept in a graph). This term does not change regardless of the value of t, making it a constant, not a variable.
In the equation f(t) = 4t + 9, t is the independent variable, as its value can be freely chosen and does not rely on any other variable in the equation. Meanwhile, f is the dependent variable, whose value depends on the input t. The numbers 4 and 9 are constants, with 4 being the coefficient of t and 9 being the constant term in the equation.
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