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spoke
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arent linear functions always constant?
espen180 said:No, they aren't. Concider for example f(x)=x.
Office_Shredder said:A constant function is a function which always takes the same value, for example f(x)=2.
All linear functions on Rncan be written as y=Ax where A is a matrix (in one dimension, just a number)
Bacle2 said:Your right, Dickfore, but your example is that of a map from ℝ to itself may be too
specific for a general definition of function.
A nonconstant linear function is a mathematical function that can be represented by a straight line on a graph. It can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. Unlike a constant linear function, a nonconstant linear function has a changing slope and is not a horizontal or vertical line.
A nonconstant linear function is different from a constant linear function in that it has a changing slope, while a constant linear function has a constant slope. This means that the graph of a nonconstant linear function will be a slanted line, while the graph of a constant linear function will be a straight horizontal or vertical line.
The slope of a nonconstant linear function is the rate of change of the function. It represents the amount by which the output (y-value) changes for every unit increase in the input (x-value). The slope can be calculated using the formula (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are any two points on the line.
To graph a nonconstant linear function, you can plot a few points by choosing different values for x and solving for y using the function's equation. Then, you can plot these points on a coordinate plane and draw a straight line through them. Alternatively, you can use the slope and y-intercept of the function to find two points on the line and then plot and connect them.
Nonconstant linear functions can be found in many real-life situations, such as calculating the cost of a taxi ride (where the cost is based on the distance traveled), determining the growth of a plant over time (where the height of the plant increases at a constant rate), or predicting the value of a stock over time (where the value changes based on various factors). These are just a few examples, but nonconstant linear functions can be used to model a wide range of real-world phenomena.