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What is constant variation in math?
Constant variation is a relationship between two variables where one is a fixed multiple of the other. The graph of such a relationship is a straight line through the origin.
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.
Is every relationship whose graph passes through the origin direct variation?
No, not every relationship whose graph passes through the origin represents direct variation. Direct variation specifically means that the relationship can be expressed in the form ( y = kx ), where ( k ) is a non-zero constant. While a graph passing through the origin indicates a proportional relationship, it can also represent other types of relationships, such as quadratic or polynomial functions, if they contain additional terms. Therefore, the key characteristic of direct variation is the constant ratio between ( y ) and ( x ), not just the point of intersection at the origin.
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.
The graph of an inverse proportion is?
hyperbola
What does the graph of an inverse variation look like?
A hyperbola.
Does the graph of an inverse variation pass through the origin?
Inverse variation does not pass through the origin, however direct variation always passes through the origin.
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.
How can you know if a graph represents a proportional relationship?
It is a relationship of direct proportion if and only if the graph is a straight line which passes through the origin. It is an inverse proportional relationship if the graph is a rectangular hyperbola. A typical example of an inverse proportions is the relationship between speed and the time taken for a journey.
How can a line graph help you investigate the relationship between two sets of data?
The general shape of the line indicates whether the relationship is linear, quadratic, polynomial, power, inverse etc. It will also help determine whether the relationship remains the same over the whole domain or changes. The scatter of the observations about a line gives a measure of the variation in the observations about the values that might be expected from the line graph.
Could you describe the shape of the graph of an inverse relationship as hyperbolic?
no you cant
What mathematical relationship between variables is suggested by a graph showing a hyperbola?
Inverse
A straight line on a graph means there is a what relationship?
A direct relationship if the slope of the line is positive. An inverse relationship if the slope of the line is negative.
What is the relationship exhibited on a gravitational force vs distance graph?
On a gravitational force vs distance graph, the relationship exhibited is an inverse square relationship. This means that as the distance between two objects increases, the gravitational force between them decreases proportionally to the square of the distance.
How can you tell if a graph has a direct relationship and an inverse relationship?
If the graph shows a direct relationship, then the line will go up. If it shows an inverse relationship, the line will go down. A direct relationship means that as one variable increases, so does the other. On a graph, this means that as we move out along one axis, we also move out along the other. An inverse relationship means that as one variable increases, the other one decreases. So, for example, as we move to the right (X increasing), we have to move down (Y decreasing).
How would you decide from a graph that the relationship was neither linear nor inverse?
because it is a methodical answer and that is why i am asking you
A graph of a complementary good in economics?
A graph of complimentary goods in economics represents the relationship between the price of of commodity & demand for it's complementary. Thus it shows a inverse relationship.
