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When is a relation considered to be function?
A relation is a function when an x value only has one y value associated with it. An easy way to tell this is to graph the relation, then draw a vertical line through it. If, at any point, it touches the graph twice, the relation isn't a function.
What is a one-to-one relation in mathematics?
A one-to-one relation in math means that for every value in the range, there's at most one value that maps to it. If you think of relations as people sitting on a bus, this means that no one is sharing a seat. More often, mathematicians talk about one-to-one functions (formally called injections) - these are just one-to-one relations that happen to be functions :-). If we write the function as y=f(x), the condition for it being one-to-one is that if f(a)=f(b), then a=b. When looking at the graph of a relation, we can determine if it's one-to-one by the horizontal line test: if any horizontal line drawn on the graph intersects the relation at most once, it is one-to-one. On the other hand, if a horizontal line intersects the relation twice, the relation is not one-to-one. For example, y=x^2 is not a one-to-one relation: (-1)^2 and 1^2 both get mapped to 1. We can see this in the graph of y=x^2 because a horizontal line above the x-axis will intersect the graph twice. y=x^3, on the other hand, is a one-to-one relation. Because the cube of a negative number stays negative, no two numbers get sent to the same number by cubing them.
What is a line that intersects a circle twice?
a chord
What is the line that intersects a circle twice?
It is called a secant line
When the graph of a quadratic function crosses the x-axis twice the x-coordinate of the lies exactly halfway between the two x-intercepts?
Exactly halfway
When is a relation considered to be function?
A relation is a function when an x value only has one y value associated with it. An easy way to tell this is to graph the relation, then draw a vertical line through it. If, at any point, it touches the graph twice, the relation isn't a function.
What is a one-to-one relation in mathematics?
A one-to-one relation in math means that for every value in the range, there's at most one value that maps to it. If you think of relations as people sitting on a bus, this means that no one is sharing a seat. More often, mathematicians talk about one-to-one functions (formally called injections) - these are just one-to-one relations that happen to be functions :-). If we write the function as y=f(x), the condition for it being one-to-one is that if f(a)=f(b), then a=b. When looking at the graph of a relation, we can determine if it's one-to-one by the horizontal line test: if any horizontal line drawn on the graph intersects the relation at most once, it is one-to-one. On the other hand, if a horizontal line intersects the relation twice, the relation is not one-to-one. For example, y=x^2 is not a one-to-one relation: (-1)^2 and 1^2 both get mapped to 1. We can see this in the graph of y=x^2 because a horizontal line above the x-axis will intersect the graph twice. y=x^3, on the other hand, is a one-to-one relation. Because the cube of a negative number stays negative, no two numbers get sent to the same number by cubing them.
Which type of line that tests for a function?
Vertical line. If you can draw a vertical line through some part of a graph and it will intersect with the graph twice, the graph isn't a function.
How can you tell if a graph show a FUNCTION?
By doing a vertical line test. If you can draw a vertical line and it only passes through the graph once, its a function. If it passes through twice, it is NOT a function.
What is a line that intersects a circle twice?
a chord
Why is the vertical line test used to determine if a graph represents a function?
The definition of a function is "A relation in which exactly one element of the range is paired with each element of the domain." This means that in the relationship of a function, each range element (x value) can only have one domain element (y value). If you draw a vertical line and it crosses your graph twice, then you can see that your x value has two y values, which is not a function.
What is the line that intersects a circle twice?
It is called a secant line
How many times will the graph of a quadratic function cross or touch the x-axis if the discriminant is positive?
It will cross the x-axis twice.
How would you know when a circle is being divide?
When another curve intersects it twice.
What does it mean when the graph of a quadratic function crosses the x axis twice?
When the graph of a quadratic crosses the x-axis twice it means that the quadratic has two real roots. If the graph touches the x-axis at one point the quadratic has 1 repeated root. If the graph does not touch nor cross the x-axis, then the quadratic has no real roots, but it does have 2 complex roots.
What test is used to determine if a graph is a function?
Horizontal line test is used for the determination of a function,if the horizontal line passes through one point of the given graph then it is a function and if it passes through more than one point then it will not a function. * * * * * No! It is a vertical line test. Consider the graph of y = sin(x): a horizontal line line will cross it twice in every 360 degrees! Convince me that y = sin(x) is not a function.
When the graph of a quadratic function crosses the x axis twice the x coordinate of the vertex lies between the two x intercepts?
that's true
