Q: What is the value of the dependent variable in a function is always?

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It is any invertible function.

You integrate the probability distribution function to get the cumulative distribution function (cdf). Then find the value of the random variable for which cdf = 0.5.

A random variable is a variable that can take different values according to a process, at least part of which is random.For a discrete random variable (RV), a probability distribution is a function that assigns, to each value of the RV, the probability that the RV takes that value.The probability of a continuous RV taking any specificvalue is always 0 and the distribution is a density function such that the probability of the RV taking a value between x and y is the area under the distribution function between x and y.

In the context of regression, it is the y-intercept: the value of the dependent variable when the independent is zero.

It will not. For the interval (x, x+dx) it may well give a non-zero probability. With a continuous distribution, the probability of any particular value is always 0. What the probability density function gives is the probability that the variable is NEAR the selected value.

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It is a value in the co-domain [range] of the function.

I found two answers for this question. A function is a rule that assigns to each value of one variable (called the independent variable) exactly one value of another variable (called the dependent variable.) A function is a rule that assigns to each input value a unique output value.

the output of a function; a variable whose value depends on the value of the input.

When it doesn't fulfill the requirements of a function. A function must have EXACTLY ONE value of one of the variables (the "dependent variable") for every value of the other variable or variables (the "independent variable").

When it doesn't fulfill the requirements of a function. A function must have EXACTLY ONE value of one of the variables (the "dependent variable") for every value of the other variable or variables (the "independent variable").

false

Use the definition of a function. If, for any value of one variable, there is only a single possible value of the second variable, then the second variable is a function of the first variable. The second variable is often called the "dependent variable". If you can solve an equation explicitly for the dependent variable, then it is a function. If you can NOT solve it for a variable, it may or may not be a function - it turns out that some equations are hard or impossible to solve explicitly for one of the variables.

It is any invertible function.

The independent variable is the variable that is altered by the scientist, and the dependent variable's value is dependent on the value of the independent variable.

the output variable is called the dependent variable. For example the function y = f(x) = 3x here x is independent and y is dependent; y changes when you change x

This will be a math function. Each choice is only going to have one answer in this kind of function.

True