no
2x-2/x^2+3x-4
y = x / (x^2 + 2x + 1) The horizontal asymptote is y = 0
-1
To determine if a function crosses its end behavior asymptote, analyze the function's behavior as ( x ) approaches positive or negative infinity. If the function's value approaches the asymptote but is not equal to it, it does not cross; however, if you find a point where the function's value equals the asymptote, it indicates a crossing. You can identify this by solving the equation of the asymptote for ( x ) and checking if the function equals that value at those ( x ) points. Graphically, plotting the function alongside the asymptote can also reveal any crossings visually.
log5x
Yes, the asymptote is x = 0. In order for logarithmic equation to have an asymptote, the value inside log must be 0. Then, 5x = 0 → x = 0.
2x-2/x^2+3x-4
7x = 5x log(7) = log(5)x = log(5) / (log(7) = 0.82709 (rounded)
The only way I ever learned to find it was to think about it. The function f(x) = log(x) only exists of 'x' is positive. As 'x' gets smaller and smaller, the function asymptotically approaches the y-axis.
y = x / (x^2 + 2x + 1) The horizontal asymptote is y = 0
It is y = 0
The explanation and answer to the following math equation to find x -0.3 plus 5-5 log (d) equals a plus 5-5 log 4 (d) is -5 log(d)+x+4.7 = a-5 log(4 d)+5. The solution is x = a-6.63147.
-1
Yes. Take the functions f(x) = log(x) or g(x) = ln(x) In both cases, there is a vertical asymptote where x = 0. Because a number cannot be taken to any power so that it equals zero, and can only come closer and closer to zero without actually reaching it, there is an asymptote where it would equal zero. Note that transformations (especially shifting the function left and right) can change the properties of this asymptote.
log5x
To determine if a function crosses its end behavior asymptote, analyze the function's behavior as ( x ) approaches positive or negative infinity. If the function's value approaches the asymptote but is not equal to it, it does not cross; however, if you find a point where the function's value equals the asymptote, it indicates a crossing. You can identify this by solving the equation of the asymptote for ( x ) and checking if the function equals that value at those ( x ) points. Graphically, plotting the function alongside the asymptote can also reveal any crossings visually.
[log2 (x - 3)](log2 5) = 2log2 10 log2 (x - 3) = 2log2 10/log2 5 log2 (x - 3) = 2(log 10/log 2)/(log5/log 2) log2 (x - 3) = 2(log 10/log 5) log2 (x - 3) = 2(1/log 5) log2 (x - 3) = 2/log 5 x - 3 = 22/log x = 3 + 22/log 5