Q: What is the definition of a linear function?

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No. A function need not be linear. For example, y = sin(x) is a function of x but it is not a linear equation.

No, I don't think that would fit the definition of a linear function.

No a linear equation are not the same as a linear function. The linear function is written as Ax+By=C. The linear equation is f{x}=m+b.

Assuming the domain is unbounded, the linear function continues to be a linear function to its end.

No. An exponential function is not linear. A very easy way to understand what is and what is not a linear function is in the word, "linear function." A linear function, when graphed, must form a straight line.P.S. The basic formula for any linear function is y=mx+b. No matter what number you put in for the m and b variables, you will always make a linear function.

No a linear equation are not the same as a linear function. The linear function is written as Ax+By=C. The linear equation is f{x}=m+b.

It will just be the gradient of the function, which should be constant in a linear function.

No. Only a linear function has a constant rate of change.No. Only a linear function has a constant rate of change.No. Only a linear function has a constant rate of change.No. Only a linear function has a constant rate of change.

it is impossible for a linear function to not have a y-intercept

As a linear function

Your age is a linear function (of time).

It is a continuous function. If the line is a straight line, it is a linear function.