How do you graph and find the discontinuities of #y=(3x) /( 4-x^2)#?
For discontinuities you first look at the denominator.
By signing up, you agree to our Terms of Service and Privacy Policy
To graph and find the discontinuities of the function y = (3x) / (4 - x^2), follow these steps:
-
Determine the domain of the function by identifying the values of x that make the denominator (4 - x^2) equal to zero. In this case, the denominator is a difference of squares, so set it equal to zero and solve for x: 4 - x^2 = 0 x^2 = 4 x = ±2
Therefore, the domain of the function is all real numbers except x = ±2.
-
Next, find the y-intercept by substituting x = 0 into the equation: y = (3(0)) / (4 - (0)^2) y = 0
The y-intercept is (0, 0).
-
To find the x-intercepts, set y = 0 and solve for x: 0 = (3x) / (4 - x^2) 3x = 0 x = 0
The x-intercept is (0, 0).
-
Determine the vertical asymptotes by analyzing the behavior of the function as x approaches the values that make the denominator zero. In this case, x = ±2 are the values that make the denominator zero. As x approaches ±2, the function approaches positive or negative infinity, respectively.
-
Sketch the graph using the information obtained. The graph will have a vertical asymptote at x = -2 and x = 2, and it will pass through the point (0, 0).
Note: The graph will have a hole at (2, 3/4) and (-2, -3/4) due to the simplification of the function.
This is the comprehensive answer to your question.
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.

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