The range is the y, while the domain is the x.
It is a bijection [one-to-one and onto].
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.
It will just be the gradient of the function, which should be constant in a linear function.
It is a continuous function. If the line is a straight line, it is a linear function.
The function is a simple linear function and so its nature does not limit the domain or range in any way. So the domain and range can be the whole of the real numbers. If the domain is a proper subset of that then the range must be defined accordingly. Similarly, if the range is known then the appropriate domain needs to be defined.
It is a bijection [one-to-one and onto].
The function ( f(x) = -3x + 6 ) is a linear function. Its domain is all real numbers, expressed as ( (-\infty, \infty) ). The range is also all real numbers, as linear functions can take any value depending on the value of ( x ). Therefore, both the domain and range are ( (-\infty, \infty) ).
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.
Yes, a linear function can be continuous but not have a domain and range of all real numbers. For example, the function ( f(x) = 2x + 3 ) is continuous, but if it is defined only for ( x \geq 0 ), its domain is limited to non-negative real numbers. Consequently, the range will also be restricted to values greater than or equal to 3, demonstrating that linear functions can have restricted domains and ranges while remaining continuous.
It will just be the gradient of the function, which should be constant in a linear function.
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).
No. A function need not be linear. For example, y = sin(x) is a function of x but it is not a linear equation.