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First of all, many relationships are inherently linear. For example, distance travelled is a linear function of time where the slope is speed.
Beyond that, linear functions are extremely simple. Because of this they can be used to model pieces of more complicated functions in a simple way. Thus, you can study the properties of the complicated function by studying a piece of it at a time, in a sense.
Many mathematical objects can be said to behave as linear operators. This means that a firm undertstanding of lines, slopes and linear functions transfers to these objects.
Linearity is fundamental to a great deal of mathematics.
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Is circumference a linear function of diameter?
circumference = pi*d so it is a linear function. If d is multiplied by x, so is the circumference.
How are linear equations and functions alike?
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
What is a linear function that goes through the origin?
it is just that- a linear function that goes through ther origin. ======================================================= Any equation y = ax, where a is a constant, will do so.
Are all linear equations functions why or why not?
The equation x=c where c is a constant is the equation of a vertical line. It can't be a function but it is linear so the answer is no. For example, the vertical line produced by the linear equation x = 3 does not represent a function. We cannot write this equation so that y is a function of x because the only x-value is 3 and this "maps" to every real-number y.
Is 3x plus 27 equals 8 a quadratic function?
No it is a linear one. X^2 = quadratic, x = linear. So if the equation doesn't have an x squared, then it is not quadratic.
Is circumference a linear function of diameter?
circumference = pi*d so it is a linear function. If d is multiplied by x, so is the circumference.
What distinguishes a linear function from other functions?
A linear function is one in which the power of the function is only one. So, the graph of it would be a straight line. For example, x2 + x = y is not linear, because the highest power is 2. A main difference is, non linear functions have curves, where as a linear function is a straight line, with the exception of when the function has a power of 0, and it is technically a straight line.
What is a linear function that goes through the origin?
it is just that- a linear function that goes through ther origin. ======================================================= Any equation y = ax, where a is a constant, will do so.
How are linear equations and functions alike?
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
How can you tell if a linear appoximation is too large or too small?
The precision of a linear approximation is dependent on the concavity of the function. If the function is concave down then the linear approximation will lay above the curve, so it will be an over-approximation ("too large"). If the function is concave up then the linear approximation will lay below the curve, so it will be an under-approximation ("too small").
Are all linear equations functions why or why not?
The equation x=c where c is a constant is the equation of a vertical line. It can't be a function but it is linear so the answer is no. For example, the vertical line produced by the linear equation x = 3 does not represent a function. We cannot write this equation so that y is a function of x because the only x-value is 3 and this "maps" to every real-number y.
Why was the cimarron cutoff so important?
It was a shortcut that avoided steep slopes but passed through deadly desert to the south.
Is 3x plus 27 equals 8 a quadratic function?
No it is a linear one. X^2 = quadratic, x = linear. So if the equation doesn't have an x squared, then it is not quadratic.
How can you tell by looking at the graph of a function that it is nonlinear?
A linear function would be represented by a straight line graph, so if it's not a straight line, it's nonlinear
How do you find the average rate of change for a linear function?
A linear function has a constant rate of change - so the average rate of change is the same as the rate of change.Take any two points, A = (p,q) and B = (r, s) which satisfy the function. Then the rate of change is(q - s)/(p - r).If the linear equation is given:in the form y = mx + c then the rate of change is m; orin the form ax + by + c = 0 [the standard form] then the rate is -a/b.
What is the difference between a linear and exponential function?
A linear function grows ( or shrinks) at a constant rate called its slope.An exponential function grows ( or shrinks) at a rate which increases(or decreases)over time. From a practical standpoint linear growth (or shrinkage) is simple and predictable. Exponential growth is essentially out of control and unsustainableand exponential decay soon becomes negligible.if y=az + b then y is a linear function of z. If y=aebz then y is an exponential function of z. If y= acbz then y is still an exponential function of z because you can substitute c=ek (so that k=logec) to give you y=aekbz .
Why is it important to have a healthy brain?
It is important to have a healthy brain so you can function correctly
