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Is there an instance when a linear equation is not a function?
Yes, a vertical line is linear, but it is not a function, because every point on the line has the same x value.
Why does the graph of a function never has two different points with the same x-coordinate?
That is simply a result of the definition of a function. A function is a mapping such that for each value of x there is only one value of y.
Which digit in 12.32 has the same place value as the 6 in 5.678?
The six is the first after the decimal point, so it corresponds to the 3.
Is an equation a function if it has more than one x value for every y value?
Yes. If it had more than one y value for each x value, on the other hand, it would not. A function is "Something that has a value depending on some input". Now an equation is something like Function(of x) = 0. You could say this equation has 2 possible values, True or False. This is not the same thing as saying there are two values of x to make the zero. So y=x2 has two values of x for every y. Generally, nobody would say y=x2 is a function. Except in the sense that it the equation is true for some values of x and y, and false for any others.
Why is the zero of a function the same as an x-intercept of a function?
when you have a function lets say y = mx + b then you set it equal to zero and solve you are finding the x values that give you a y value of zero and a y value of zero lies on the x-axis. therefore when you find a zero of a function it's really the x value of where the function touches or crosses the x axis. hope this helps
Why doesnt the graph of a function have two different points with the same x coordinate?
That's how "function" is defined. If you have two points with the same x-coordinates, you have a "relation", but not a "function". A function is a special type of relation. The idea of a function is that, for every value of the independent variable (for example, "x"), the dependent variable (for example, "y") is uniquely defined. In other words, you can consider a function as a rule that assigns a y-value uniquely to every x-value.
What is a relationship in which each input value corresponds to exactly one output value?
This type of relation is called a function (a simpler way to remember it is only one Y value for every X value).In functions where there are turning points (local maxima or minima), different x-values will map onto the same y-value. However, if each x-value has exactly one y-value, then the function will either be increasing for all x ordecreasing for all x.Such functions are called monotonic functions.
Is there an instance when a linear equation is not a function?
Yes, a vertical line is linear, but it is not a function, because every point on the line has the same x value.
What is eigenfunction?
when an operator operate on a function and same function is reproduced with some numerical value then the function is called eigenfunction and the numerical value is called eigen value.
Why does the graph of a function never has two different points with the same x-coordinate?
That is simply a result of the definition of a function. A function is a mapping such that for each value of x there is only one value of y.
Which digit in 12.32 has the same place value as the 6 in 5.678?
The six is the first after the decimal point, so it corresponds to the 3.
What does function of x equals function of -x mean?
It means that the value of the function at any point "x" is the same as the value of the function at the negative of "x". The graph of the function is thus symmetrical around the y-axis. Examples of such functions are the absolute value, the cosine function, and the function defined by y = x2.
Can two different x values have the same Y value?
Yes, depending on the function. For example, in the function y = x squared, for x-values of both 2 and -2 you get the same y-value.
Can a pair with the same x and y value be a function?
Yes; a line at 45 degrees.
Is -7 a function?
Any number can be considered a function - a constant function, to be more precise. That is, the value of the function is the same for all values of "x" or whatever you call your independent variable or variables.
Is an equation a function if it has more than one x value for every y value?
Yes. If it had more than one y value for each x value, on the other hand, it would not. A function is "Something that has a value depending on some input". Now an equation is something like Function(of x) = 0. You could say this equation has 2 possible values, True or False. This is not the same thing as saying there are two values of x to make the zero. So y=x2 has two values of x for every y. Generally, nobody would say y=x2 is a function. Except in the sense that it the equation is true for some values of x and y, and false for any others.
What every day object has the same function as the nucleus in a plant or aniaml cell?
merp
