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Why does line parallel to the x-axis will intersect the graph of a function once at most if the function has an inverse?
Suppose you have a function y = f(x) which has an inverse.
Therefore there exists a function g(y) such that g(y) = x whenever y = f(x).
Now suppose a line parallel to the x axis, y = k (some constant), intersects the graph of y = f(x) at more than one point: say x1 and x2. That means that k = f(x1) and k = f(x2).
Now, in the context of the function g, this means that
[from the first intersection] g(k) = x1
and
[from the first intersection] g(k) = x2
But the function g cannot map k to two different points.
That is the contradiction which precludes the possibility of a horizontal line intersecting an invertible function more than once.
What else can I help you with?
Will the graph of a system of parallel lines intersect at exactly 1 point?
Parallel lines don't intersect, no matter how many of them there are.
How can you graph the inverse of a function without finding the ordered pairs first?
To graph the inverse of a function without finding ordered pairs, you can reflect the original graph across the line ( y = x ). This is because the coordinates of the inverse function are the swapped coordinates of the original function. Thus, for every point ( (a, b) ) on the original graph, the point ( (b, a) ) will be on the graph of its inverse. Ensure that the original function is one-to-one for the inverse to be valid.
Function and inverse of function graph is the same?
In general the function and it inverse are not the same and do not have the same graph. If we look at a special function f(x)=x, it is equal to its inverse and the graph is the same. Think of the inverse of a function as changing all the x's to y's and vice versa. Well, in the function f(x)=x, all the x's are already y's and vice versa so it is its own invese.
Graph of an inverse proportion is an?
The graph of the function y(x) = 1/x is a hyperbola.
0 pi is not a point on the graph of which inverse function?
Arcsin
Will the graph of a system of parallel lines intersect at exactly 1 point?
Parallel lines don't intersect, no matter how many of them there are.
What is the relationship between a logarithmic function and its corresponding graph in terms of the log n graph?
The relationship between a logarithmic function and its graph is that the graph of a logarithmic function is the inverse of an exponential function. This means that the logarithmic function "undoes" the exponential function, and the graph of the logarithmic function reflects this inverse relationship.
Function and inverse of function graph is the same?
In general the function and it inverse are not the same and do not have the same graph. If we look at a special function f(x)=x, it is equal to its inverse and the graph is the same. Think of the inverse of a function as changing all the x's to y's and vice versa. Well, in the function f(x)=x, all the x's are already y's and vice versa so it is its own invese.
Does a constant function intersect the x axis?
Only if y = 0 then it is the entire x-axis. Otherwise, for y = k and k is any number except zero, the graph is parallel to the x-axis and does not intersect.
Graph of an inverse proportion is an?
The graph of the function y(x) = 1/x is a hyperbola.
What can be used to determine if a graph represents a function?
If the graph is a function, no line perpendicular to the X-axis can intersect the graph at more than one point.
0 pi is not a point on the graph of which inverse function?
Arcsin
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 do you tell if a graph is a function?
For a 2-dimensional graph if there is any value of x for which there are more than one values of the graph, then it is not a function. Equivalently, any vertical line can intersect the a function at most once.
How can you tell if a equation is inverse?
Graph that equation. If the graph pass the horizontal line test, it is an inverse equation (because the graph of an inverse function is just a symmetry graph with respect to the line y= x of a graph of a one-to-one function). If it is given f(x) and g(x) as the inverse of f(x), check if g(f(x)) = x and f(g(x)) = x. If you show that g(f(x)) = x and f(g(x)) = x, then g(x) is the inverse of f(x).
How can you tell if one function is the inverse of another?
draw them both out on a graph and then draw the line y=x through the origin. If one function is a reflection of the other, it is the inverse
Graph Inverse function of the exponential function?
An exponential function is of the form y = a^x, where a is a constant. The inverse of this is x = a^y --> y = ln(x)/ln(a), where ln() means the natural log.
