Because the logarithm is its inverse, it will have a vertical asymptote.
Answer and Explanation:
Logarithmic functions do not have horizontal asymptotes. Logarithmic functions have vertical asymptotes.
5) Does the graph of a general logarithmic function have a horizontal asymptote? Explain. No. A horizontal asymptote would suggest a limit on the range, and the range of any logarithmic function in general form is all real numbers.
The natural log function, f(x) = ln(x) does not have a horizontal asymptote. In general, we have the following rule regarding the asymptotes of logarithmic functions: Any logarithmic function of the form y = logb (x) has a vertical asymptote of x = 0, and it has no horizontal asymptotes.
The graphs of rational functions are characterized by asymptotes. Asymptotes are lines that the curve approaches at the edges of the coordinate plane. Vertical asymptotes occur where the denominator of a rational function approaches zero.
Vertical asymptotes are "holes" in the graph where the function cannot have a value. They stand for places where the x-value is not allowed. Specifically, the denominator of a rational function cannot be equal to zero. Any value of x that would make the denominator equal to zero is a vertical asymptote.
Horizontal asymptotes exist for functions where both the numerator and denominator are polynomials. These functions are called rational expressions.
To determine the vertical asymptotes of a rational function, all you need to do is to set the denominator equal to zero and solve. Vertical asymptotes occur where the denominator is zero. Remember, division by zero is a no-no. Because you can't have division by zero, the resultant graph thus avoids those areas.
Recall that an exponential function has a horizontal asymptote. Because the logarithm is its inverse, it will have a vertical asymptote. The general form of a logarithmic function is f ( x ) = a log b ( x − h ) + k and the vertical asymptote is .
Vertical Asymptotes. If the limit of f(x) as x approaches c from either the left or right (or both) is ∞ or −∞, we say the function has a vertical asymptote at c.
So the tangent will have vertical asymptotes wherever the cosine is zero. Sticking to the same intervale of −π to 2π, the vertical asymptotes will be at −π/2, π/2, and 3π/2. In other words, there will be a vertical asymptote midway between each multiple of π.
The graph of a logarithmic function has a vertical asymptote at x = 0. The graph of a logarithmic function will decrease from left to right if 0 < b < 1. And if the base of the function is greater than 1, b > 1, then the graph will increase from left to right.
Example: Graph of y= 1/x has Y axis as the vertical asymptote. Since at x=0, y is undefined. Similarly any x terms present in denominator give rise to vertical asymptote when denominator is zero. So, absence of vertical asymptote implies, there is no such x, which makes y infinity.
The rational function f(x) = P(x) / Q(x) in lowest terms has no horizontal asymptotes if the degree of the numerator, P(x), is greater than the degree of denominator, Q(x).
The difference between log and ln is that log is defined for base 10 and ln is denoted for base e. For example, log of base 2 is represented as log2 and log of base e, i.e. loge = ln (natural log).
The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459.
"When the degree of the numerator of a rational function is less than the degree of the denominator, the x-axis, or y=0, is the horizontal asymptote. When the degree of the numerator of a rational function is greater than the degree of the denominator, there is no horizontal asymptote."
Answer and Explanation:
A logarithmic function can have a y-intercept if it is of the form y = l o g b ( x ± c ) , and its vertical asymptote is placed before the y-axis, meaning its asymptote is of the form x = a, where a < 0.
If the domain of a logarithmic function includes zero then the function has the y-intercept. Otherwise, the function does not have the y-intercept. For example, the function f ( x ) = l o g ( 2 x ) does not have the y-intercept since 0 is not in its domain.
In general, the logarithmic function:
always has positive x, and never crosses the y-axis. always intersects the x-axis at x=1 ... in other words it passes through (1,0)