How do you graph #y= (2x)/(x-1)#?
To graph the equation y = (2x)/(x-1), we can follow these steps:
-
Determine any restrictions on the domain. In this case, the function is undefined when the denominator (x-1) equals zero. So, x cannot be equal to 1.
-
Find the y-intercept by substituting x = 0 into the equation: y = (2(0))/(0-1) = 0
-
Determine the x-intercept by substituting y = 0 into the equation and solving for x: 0 = (2x)/(x-1) 2x = 0 x = 0
-
Plot the intercepts on the graph.
-
Analyze the behavior of the function as x approaches positive and negative infinity. As x approaches infinity, y approaches 2. As x approaches negative infinity, y also approaches 2.
-
Determine the vertical asymptote by finding the values of x that make the denominator equal to zero. In this case, x = 1 is the vertical asymptote.
-
Sketch the graph, considering the intercepts, asymptote, and the behavior of the function.
The graph of y = (2x)/(x-1) will have a y-intercept at (0, 0), an x-intercept at (0, 0), a vertical asymptote at x = 1, and the function will approach y = 2 as x approaches positive and negative infinity.
By signing up, you agree to our Terms of Service and Privacy Policy
Graph as
by establishing a few data points with random values of
help give shape to the graph
graph{(2x)/(x-1) [-25.3, 26, -11.27, 14.4]}
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How do you solve #7/(8x) + 3/(5x) = 1 #?
- How do you graph #(2x^2) /( x^2 - 9)#?
- There are 78 cyclists at the park. If the ratio of cyclists to skaters is 3 to 1, how many skaters are at the park?
- How do you divide #( -x^3 - 6x^2+3x+4 )/(2x^2 - x )#?
- How do you multiply #(3x-15)/(4x^2-2x)*(10x-20x^2)/(5-x)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7