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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.
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Is the inverse of the function y x2 still a function?
Y = 1/X2 ==============Can it pass the line test? * * * * * That is not the inverse, but the reciprocal. Not the same thing! The inverse is y = sqrt(x). Onless the range is resticted, the mapping is one-to-many and so not a function.
Is graph and chart similar?
In statistics, a graph and a chart are the same. In arithmetic, a graph is the plot of a function over values. There are no charts.
Why it is valid to say that both a function and its inverse describe the same relationship.?
If a function has an inverse then it is a bijection between two sets. Each element in the first set is mapped to one, and only one, element of the second set. Therefore, for each element in the second set there is one, and only one, element in the first set. The function and its inverse, both define the relationship between the same pairs of elements.
What test determines if a function is one to one?
First recall that a function is one to one if no two elements in its domain have the same element in the range One trick to finding out if a function is one to one is to use the Horizontal line test. You may view the link for a better explanation. The main idea is if a horizontal line intersects the graph of a function more than one time, then the function is not one to one. This is important because if it is not one to one, it has no inverse.
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 you determine whether the inverse of a function is a function by using vertical line test?
Not quite. You can use a vertical line test on the graph of the inverse mapping, OR you can use a horizontal line test on the original graph. The horizontal line test is used in the same way.
Is the inverse of the function y x2 still a function?
Y = 1/X2 ==============Can it pass the line test? * * * * * That is not the inverse, but the reciprocal. Not the same thing! The inverse is y = sqrt(x). Onless the range is resticted, the mapping is one-to-many and so not a function.
How can you tell whether a graph is a function or not?
A vertical line test can be used to determine whether a graph is a function or not. If a vertical line intersects the graph more than once, then the graph is not a function.
An exponential function is the inverse of a logarithmic function?
Yes, y = loga(x) means the same as x=ay.
What do you call a function whose graph is a non-vertical line?
It is a function. If the graph contains at least two points on the same vertical line, then it is not a function. This is called the vertical line test.
What is the relationship between the domains and ranges of a function and its inverse?
The domain of a function, f(x), is a set of real numbers (call them values of x) which corresponds to a second set, called the range, such that each element in the domain corresponds to exactly one element in the range ( y- value). So the range is the set of real numbers that are values of the function. An inverse of a function f(x) is denoted by f-1(x) where -1 is NOT an exponent. The notation f-1 does not mean 1/f (so it looks like a neg 1 exponent but it is not. Math people know to read this as the inverse function). Any function that passes the horizontal line test (which intersects the graph of the function only once) has an inverse, also it is a one-to-one function. Any one-to-one function has a graph that passes the horizontal line test. A one-to one function is a function in which not two different pairs have the same second component. For this kind of functions (one-to-one functions), the domain becomes the range for the inverse and vv. It means that if a point (x, y) is on the graph of f, then the point (y, x) is on the graph of f-1. Ex: y or f(x) = x2 (the domain is the set of all real numbers. you can square positives, negatives, fractions etc. the range is only all reals greater than or equal to zero). The graph of f(x) = x2 does not pass the horizontal test, because it intersects the graph at two points, let's say (-3, 9) and (3, 9). Inverse functions have ordered pairs with the coordinates reversed. If we interchange x- and y-coordinates then we obtain (9, -3) and (9, 3) but these ordered pairs do not define a function. Thus this function does not have an inverse. But if we restrict the domain, for example the set of all positive numbers including zero, then we allow it to have one, and this inverse function f-1 is a reflection of the graph of f about the line y = x, where f(x) = x2 and its domain is {x| x ≥ 0}. The inverse of the above function is the square root of x. which I will abbreviate as sq rt the inverse function becomes f-1(x) = √x (in other words, f you limit yourself to real numbers, you cannot use any negatives in place of x for this inverse function. So the domain of the inverse is all reals > or = 0. If the inverse is to be a function you cannot have any answers which are negative. the relation would not pass the vertical line test. so the range is also only reals > or = zero).
Is graph and chart similar?
In statistics, a graph and a chart are the same. In arithmetic, a graph is the plot of a function over values. There are no charts.
Why it is valid to say that both a function and its inverse describe the same relationship.?
If a function has an inverse then it is a bijection between two sets. Each element in the first set is mapped to one, and only one, element of the second set. Therefore, for each element in the second set there is one, and only one, element in the first set. The function and its inverse, both define the relationship between the same pairs of elements.
A logarithmic function is the same as an exponential function?
Apex: false A logarithmic function is not the same as an exponential function, but they are closely related. Logarithmic functions are the inverses of their respective exponential functions. For the function y=ln(x), its inverse is x=ey For the function y=log3(x), its inverse is x=3y For the function y=4x, its inverse is x=log4(y) For the function y=ln(x-2), its inverse is x=ey+2 By using the properties of logarithms, especially the fact that a number raised to a logarithm of base itself equals the argument of the logarithm: aloga(b)=b you can see that an exponential function with x as the independent variable of the form y=f(x) can be transformed into a function with y as the independent variable, x=f(y), by making it a logarithmic function. For a generalization: y=ax transforms to x=loga(y) and vice-versa Graphically, the logarithmic function is the corresponding exponential function reflected by the line y = x.
What test determines if a function is one to one?
First recall that a function is one to one if no two elements in its domain have the same element in the range One trick to finding out if a function is one to one is to use the Horizontal line test. You may view the link for a better explanation. The main idea is if a horizontal line intersects the graph of a function more than one time, then the function is not one to one. This is important because if it is not one to one, it has no inverse.
If the parents function is y4x which is the function of the graph?
The function y = x is the graph that passes from the points (-1, -1), (0, 0), and (1, 1) The function y = 4x is the graph that passes form the points (-1, -4), (0, 0), and (1, 4) Sketch these graphs in a same x and y coordinate system, and you can see both of them
What are the 3 main characteristics of a function?
Each input has only one output. The same input will always produce the same output. The function can be represented by an equation or a graph.
