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If the graph of an equation CANNOT be intersected in more than one place by a vertical line is it a function.?
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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.
How do you tell if a function with a vertical asympote has a numerator of 1 or a numerator of x?
If there are no coordinates given then you cannot.
How are functions equation slopes and graphs related?
There are some relationships but not all relationships are always true. Any function can be represented by an equation. But all equations are not functions. For example, y = sqrt(x) is the equation of the square root relationship which can be graphed as a parabola on its side, but it is not a function. It has slopes at each point. Some functions can be plotted as graphs but not all. A function such as f(x) = 1 when x is rational, and f(x) = 0 when x is irrational has no slope and cannot be plotted as a graph. A graph of a vertical line is not a function.
How does the vertical line test determine if a graph represents a function?
Functions cannot have two y-values (outputs) for any single x-value (input), so if you can draw a vertical line that touches more than 1 point on the graph, it is not a function.
What is difference between nonlinear equation and transcendental equation?
A polynomial equation of order >1 that is, where the power of the variable is greater than 1 is a non linear function. A transcendental function is one that cannot be expressed as a finite number of algebaraic operations (addition, multiplication, roots). The exponential and trigonometric functions (and their inverses) are examples.
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.
How can you tell if a function is a function?
The vertical line test can be used to determine if a graph is a function. If two points in a graph are connected with the help of a vertical line, it is not a function. If it cannot be connected, it is a function.
How can you tell if a graph is a function?
A graph is a function if every input (x-value) corresponds to only one output (y-value). One way to check for this is to perform the vertical line test: if a vertical line intersects the graph at more than one point, the graph is not a function.
Explain why the equation of a vertical line cannot be in slope-intercept form?
A vertical line on a graph has an infinite slope, and no y-intercept.
What is vertical line test in a function?
If, at any time, a vertical line intersects the graph of a relationship (or mapping) more than once, the relationship is not a function. (It is a one-to-many mapping and so cannot be a function.)
What is the slope intercept form when a vertical line is passing through 5 -8?
The slope of a vertical line is undefined and so there cannot be a slope-intercept form of the equation.
How do you tell if a function with a vertical asympote has a numerator of 1 or a numerator of x?
If there are no coordinates given then you cannot.
Will a function always be a vertical line?
no it won't In fact a function can NEVER be vertical. Not only that, it cannot loop back so that two (or more) points are above one another. For a function, there can be at most one y-value for any x-value so any vertical line will intersect the function at most once.
How are functions equation slopes and graphs related?
There are some relationships but not all relationships are always true. Any function can be represented by an equation. But all equations are not functions. For example, y = sqrt(x) is the equation of the square root relationship which can be graphed as a parabola on its side, but it is not a function. It has slopes at each point. Some functions can be plotted as graphs but not all. A function such as f(x) = 1 when x is rational, and f(x) = 0 when x is irrational has no slope and cannot be plotted as a graph. A graph of a vertical line is not a function.
Why can you not write an equation of a vertical line?
A vertical line has the equation x = C (a constant value), where y has all values, x has only one value, and the slope is undefined (the run, Δx, is zero, so you cannot divide the rise by the run).
When you are given a graph how can you come up with a rational function equation?
You cannot, necessarily. Given a graph of the tan function, you could not.
How do you know if a graph is a function or not?
As long as the line represented on the graph has no vertical segments then it may be represented by a function. * * * * * That is not enough. y = sqrt(x) has no vertical segments but it is not a function in the mathematical sense. A function cannot map an x value to more than one y value. Clearly, the above function maps x to -sqrt(x) and +sqrt(x) and so is not a function. However, there no vertical segment. No matter how close you get to x = 0, there is still a curve and the segment is not vertical.
