how do u find the range for this equation
y=x^2+x-2/|x-1|
I went on symbolab, it says range (-3,∞), but I dont understand it
thanks
that's because the range is all real numbers
There's a vertical asymptote at x=1 which goes to -∞
After that, for x>1, the curve approaches y=x^2+x, which rises to +∞
As x→1, y→ -3, but near x=1, the asymptote takes over, and heads of down to -∞
Take a look at the graph at wolframalpha.com
I agree with oobleck
Did you perhaps mean:
y = (x^2 + x - 2)/|(x-1| ??
in that case
y = (x+2)(x-1)/|x-1|
y = x+2 or y = -x-2, but that also would not give you the answer of (-3,∞)
Actually, in this case,
for all x ≠ -1
y = (x+2)(x-1)/|x-1| =
x+2 for x > 1 ... range is (3,∞)
-x-2 for x < -1 ... range is (-3,∞)
So the range here is (-3,∞)
hi, also I understand the line x-int and y-int , but what about the other line? how did u find that
of course!
For some weird reason I was looking at the domain.
To find the range of the given equation, we first need to consider the denominator term |x-1|.
The absolute value function |x-1| can be either positive or negative, depending on the value of x in relation to 1. For x < 1, the absolute value of (x-1) will be -(x-1), and for x > 1, it will be (x-1).
Now, let's analyze the equation y = (x^2 + x - 2) / |x - 1|:
1. For x < 1:
In this case, |x - 1| = -(x - 1) = (1 - x).
When we substitute this value into the equation, we have:
y = (x^2 + x - 2) / (1 - x).
2. For x > 1:
In this case, |x - 1| = (x - 1).
When we substitute this value into the equation, we have:
y = (x^2 + x - 2) / (x - 1).
Now, let's find the range of the equation for both cases:
1. For x < 1:
We can determine the range by examining the behavior of the equation as x approaches negative infinity. For large negative values of x, the term (1 - x) becomes very large, making the denominator infinitely close to zero and tending towards negative infinity. However, the numerator, (x^2 + x - 2), can be both positive and negative.
As x approaches negative infinity, the numerator will dominate the denominator. Since the numerator can take on both positive and negative values as x gets more negative, the range of the equation is (-∞,∞).
2. For x > 1:
Similarly, we can determine the range by examining the behavior of the equation as x approaches positive infinity. For large positive values of x, the term (x - 1) becomes very large, making the denominator infinitely close to zero and tending towards positive infinity. Once again, the numerator, (x^2 + x - 2), can be both positive and negative.
As x approaches positive infinity, the numerator will dominate the denominator. Since the numerator can take on both positive and negative values as x gets larger, the range of the equation is (-∞,∞).
Combining the ranges for both cases, we find that the overall range of the given equation is (-∞,∞).