How do the graphs y= 1/x and y=5/x+6 compare
The graphs y= 1/x and y=5/x+6 compare in that they both have a negative slope and both have a y-intercept of 6. However, the graph y=5/x+6 has a steeper slope than the graph y=1/x.
Silly answer!!!
y = 1/x has no y-intercept , nor an x-intercept
also did you mean
y = 5/x + 6 or y = 5/(x+6) ?
the graph of 5/(x+6) is the same as the graph of 1/x, but
shifted left 6
scaled vertically by a factor of 5
To compare the graphs of y=1/x and y=5/x+6, we can analyze their behavior and characteristics.
First, let's examine the general form of both equations:
1) y = 1/x
2) y = 5/(x+6)
Both equations represent rational functions, which are functions that can be expressed as the ratio of two polynomials.
1) For the graph of y=1/x, we can start by creating a table of values by arbitrarily selecting x-values and calculating the corresponding y-values. For example:
x | y = 1/x
-----------------
-2 | -0.5
-1 | -1
0 | Undefined
1 | 1
2 | 0.5
Plotting these points on a coordinate plane, we can see that the graph approaches zero for large x-values, has a vertical asymptote at x=0 (since the function is undefined when x=0), and approaches zero for small x-values. The graph resembles a hyperbola opening towards the x and y-axes.
2) Turning to the equation y=5/(x+6), we can apply a similar process. Again, let's create a table of values:
x | y = 5/(x+6)
------------------
-10 | 0.2381
-5 | 0.8333
-1 | 1.6667
0 | Undefined
1 | 2.5
Plotting these points on a coordinate plane, we observe that the graph approaches zero for large x-values, has a vertical asymptote at x=-6 (since the function is undefined when x=-6), and approaches positive infinity for small x-values. The graph resembles a shifted hyperbola along both the x and y-axes.
In summary, the two graphs have similar shapes as they both represent rational functions. However, they differ in terms of their vertical asymptotes and the stretching or shifting factors. The graph of y=5/(x+6) is essentially the graph of y=1/x shifted six units to the left and vertically stretched by a factor of 5.