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A graph of a function cannot have two different coordinates (or points) with the same x-value because, by definition, a function assigns exactly one output (y-value) for each input (x-value). If a graph did have two points with the same x-coordinate but different y-coordinates, it would violate the definition of a function, as a single input would yield multiple outputs. This concept is often referred to as the "vertical line test," where any vertical line drawn on the graph intersects it at most once.
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How The graph of a function never has two different points with the same coordinate because?
The graph of a function never has two different points with the same coordinate because, by definition, each input (or x-coordinate) must correspond to exactly one output (or y-coordinate). If two points had the same x-coordinate but different y-coordinates, it would violate the fundamental property of a function, which states that each input maps to a unique output. Therefore, for a relation to be classified as a function, it must maintain this one-to-one mapping for all x-values.
How are the real solutions of a quadratic equation related to the graph of the quadratic function?
The real solutions are the points at which the graph of the function crosses the x-axis. If the graph never crosses the x-axis, then the solutions are imaginary.
What shape is the graph of a Gaussian function?
A Guassian function has a top in the middle and it's ends reach until infinity but the graph never touches the x axis. The location of the top depends on the parameters used.
Why does the graph of a function never have two different points with the same x coordinate?
The graph of a function cannot have two different points with the same x-coordinate because it would violate the definition of a function, which states that each input (x-coordinate) must correspond to exactly one output (y-coordinate). If a single x-coordinate were to map to two different y-values, it would not be a function, as there would be ambiguity in the output for that input. This unique pairing ensures that every element in the domain is associated with one and only one element in the range.
Does the graph of an exponential function have an x intercept?
No, the graph of an exponential function of the form ( f(x) = a \cdot b^x ) (where ( a > 0 ) and ( b > 0 )) does not have an x-intercept. As ( x ) approaches negative infinity, the function approaches zero but never actually reaches it, meaning the graph does not intersect the x-axis. Thus, there are no values of ( x ) for which ( f(x) = 0 ).
Is a circle graph a function?
No, a circle graph is never a function.
How The graph of a function never has two different points with the same coordinate because?
The graph of a function never has two different points with the same coordinate because, by definition, each input (or x-coordinate) must correspond to exactly one output (or y-coordinate). If two points had the same x-coordinate but different y-coordinates, it would violate the fundamental property of a function, which states that each input maps to a unique output. Therefore, for a relation to be classified as a function, it must maintain this one-to-one mapping for all x-values.
A line is an for a function if the graph of the function gets closer and closer to touching the line but never reaches it?
asymptote
How are the real solutions of a quadratic equation related to the graph of the quadratic function?
The real solutions are the points at which the graph of the function crosses the x-axis. If the graph never crosses the x-axis, then the solutions are imaginary.
Why the graph of a function never has 2 different points with the same x- coordinate because?
It is because a function is defined as a relation which cannot be one-to-many.
What shape is the graph of a Gaussian function?
A Guassian function has a top in the middle and it's ends reach until infinity but the graph never touches the x axis. The location of the top depends on the parameters used.
The graph of a function never has two different points with the same x-coordinate because?
Answer this question… each input value is mapped to a single output value. Apex
Why does the graph of a function never have two different points with the same x coordinate?
The graph of a function cannot have two different points with the same x-coordinate because it would violate the definition of a function, which states that each input (x-coordinate) must correspond to exactly one output (y-coordinate). If a single x-coordinate were to map to two different y-values, it would not be a function, as there would be ambiguity in the output for that input. This unique pairing ensures that every element in the domain is associated with one and only one element in the range.
Can the graph of a function have a point on a vertical asymptote?
No. The fact that it is an asymptote implies that the value is never attained. The graph can me made to go as close as you like to the asymptote but it can ever ever take the asymptotic value.
Is 10y equals -x a function?
Yes, because you can rewrite it as: y = -x/10 Which is a line. When you graph the above equation, the graph passes the vertical line test - meaning that the graph never intersects with any vertical line more than once.
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.
What can you say about the graph of the function below Check all that apply. F(x) (0.9)x?
The graph of the function ( F(x) = (0.9)^x ) is an exponential decay function. As ( x ) increases, the value of ( F(x) ) decreases towards zero but never actually reaches it, resulting in a horizontal asymptote at ( y = 0 ). Additionally, the graph is always positive for all real values of ( x ). The function starts at ( F(0) = 1 ) and decreases as ( x ) moves to the right.
