compare the graphs of the inverse variations by comparing asymptotes, similar points, lines of reflections and quadrants
y=-0.7/x and y=-0.9/x
Steve can you explain this problem
How owuld you answer this question I know they are in different quadrants but look the same in opposite directions
To compare the graphs of inverse variations represented by the equations y = -0.7/x and y = -0.9/x, we can examine their asymptotes, similar points, lines of reflection, and quadrants.
Asymptotes:
For inverse variation equations of the form y = k/x, where k is a constant, the vertical asymptote is the line x = 0, and the horizontal asymptote is the line y = 0. In both equations y = -0.7/x and y = -0.9/x, the vertical asymptote is x = 0, and the horizontal asymptote is y = 0.
Similar Points:
To find similar points, we can choose different x-values and calculate their corresponding y-values. Let's calculate the values for some x-values:
For y = -0.7/x:
When x = 1, y = -0.7/1 = -0.7
When x = 2, y = -0.7/2 = -0.35
When x = 3, y = -0.7/3 ≈ -0.233
For y = -0.9/x:
When x = 1, y = -0.9/1 = -0.9
When x = 2, y = -0.9/2 = -0.45
When x = 3, y = -0.9/3 ≈ -0.3
From these calculations, we can see that for the same x-values, the graphs of the two equations have different y-values, indicating that the graphs are not identical.
Lines of Reflection:
The graphs of inverse variations are symmetric with respect to the lines y = x and y = -x. If we swap the x and y variables in the inverse variation equations, we can obtain equations representing the reflection of the original graph.
For y = -0.7/x, swapping x and y gives x = -0.7/y. We can rewrite this equation as y = -0.7/x, revealing that the graph of y = -0.7/x is its own reflection.
For y = -0.9/x, swapping x and y gives x = -0.9/y. We can rewrite this equation as y = -0.9/x, showing that the graph of y = -0.9/x is also its own reflection.
Therefore, both equations have lines of reflection that coincide with the original graphs.
Quadrants:
To determine the quadrants of the graphs, we need to consider the signs of x and y.
For y = -0.7/x, when x is positive, y is negative, and vice versa. So, the graph of this equation will lie in the 2nd and 4th quadrants.
For y = -0.9/x, when x is positive, y is negative, and vice versa. So, the graph of this equation will also lie in the 2nd and 4th quadrants.
In summary, the graphs of y = -0.7/x and y = -0.9/x have the same asymptotes (x = 0 and y = 0), different y-values for the same x-values, lines of reflection that coincide with their original graphs, and they both lie in the 2nd and 4th quadrants.