Compare the graphs of the inverse variations. Please provide at least 3 comparisons.
y = -0.2/x and y= -0.3/x.
i found -0.1/x , -0.15/x?
and -0.04/x, -0.06/x
and -0.0222/x , -0.0333/x
i'm not sure if i need to put " /x" every time at the end but i just wanted to know if my answers were correct please?
Go on :
wolframalpha.c o m
When page be open in rectangle type:
plot y = - 0.2 / x , y = - 0.3 / x
and click option =
You will see graphs.
Some comparisons:
both are not defined for x = 0
both are hyperbolas
both have the same asymptotes: the y-axis,
both have the same limits when x→ 0 by the right and by the left: ±∞
both have the same limits when x→ ±∞: zero.
they never touch one to each other
so i went on the website you told me to go on.
i put the plot that you told me to and it gave me graphs but it didn't give me no comparison or anything just 3 graphs. so i'm a bit confused here
wolframalpha does not make a comparison.
From the graphs it's obvious what I wrote about the functions.
so the same limits... and the same asymptotes was the answer?
To compare the graphs of inverse variations, you can analyze the behavior of the equations as the input variable, x, changes. In inverse variations of the form y = k/x, where k is a constant, the graph will have certain characteristics:
1. As x increases, y decreases, and vice versa: In both equations y = -0.2/x and y = -0.3/x, as x increases, y decreases, and as x decreases, y increases. This is a common characteristic of inverse variations.
2. The graphs have a vertical asymptote at x = 0: In both equations, when x approaches 0, y approaches infinity or negative infinity. This means that the graphs will have a vertical asymptote at x = 0, where the graph is undefined.
3. The graphs have a negative slope: In both equations, the constant term before the fraction, -0.2 and -0.3, is negative. This means that as x increases, the value of y decreases at a faster rate, resulting in a negative slope for the graph.
Now, let's check the comparisons you provided:
- For the inputs -0.1, -0.15, -0.04, and -0.06, the corresponding values for both equations should be the same. However, since you mentioned "-0.1/x", "-0.15/x", "-0.04/x", and "-0.06/x", it seems that you mistakenly applied the division by x at the end of each term. You don't need to divide by x when comparing the values directly. You should check the values without the division to ensure accuracy.
- Similarly, for the inputs -0.0222 and -0.0333, you don't need to include the "/x" term when comparing values.
To determine the correct comparisons for the equations y = -0.2/x and y = -0.3/x, you should substitute different values of x into each equation separately and directly compare the resulting y-values.
For example:
- When x = 1:
Equation 1: y = -0.2/1 = -0.2
Equation 2: y = -0.3/1 = -0.3
- When x = 2:
Equation 1: y = -0.2/2 = -0.1
Equation 2: y = -0.3/2 = -0.15
By comparing the calculated values, you can determine whether the equations have the same or different outputs for the same inputs. This will lead to accurate comparisons of the inverse variation graphs.