When can a graph cross a horizontal asymptote?

When can a graph cross a horizontal asymptote?

A curve may cross its asymptote any number of times, including 0 (that is, not crossing) and infinite times. For example, the graph of the function y = (sinx)/x. It crosses the horizontal asymptote y = 0 infinite times.

Is it possible for the graph of a rational function to intersect its horizontal asymptote?

Notice that, while the graph of a rational function will never cross a vertical asymptote, the graph may or may not cross a horizontal or slant asymptote. Also, although the graph of a rational function may have many vertical asymptotes, the graph will have at most one horizontal (or slant) asymptote.

How do you know if the graph will cross the horizontal asymptote?

The graph of f cannot intersect its vertical asymptote. The graph of f can intersect its horizontal asymptote. As x → ± ∞, f(x) → y = ax + b, a ≠ 0 or The graph of f can intersect its horizontal asymptote.

Can an asymptote intersection a function?

It is impossible for the graph of a function to intersect a vertical asymptote (or a vertical line in general) in more than one point. Moreover, if a function is continuous at each point where it is defined, it is impossible that its graph does intersect any vertical asymptote.

What is the horizontal asymptote of an exponential function?

Properties of Exponential Graphs The function y=bx y = b x has the x -axis as a horizontal asymptote because the curve will always approach the x -axis as x approaches either positive or negative infinity, but will never cross the axis as it will never be equal to zero.

What is important to look at when determining horizontal asymptotes?

When you are determining the horizontal asymptotes, it is important to consider both the right and the left hand sides, because the horizontal asymptotes will not necessarily be the same in both places. Consider the reciprocal function and note how as x goes to the right and left it flattens to the line y=0.

Do logs have horizontal asymptotes?

So here’s what I “know”—the logarithm is just the inverse of the exponential function, and the exponential function doesn’t have any vertical asymptotes—you can always exponentiate a larger number. Thus, it should be that when you invert this function to form the logarithm, there shouldn’t be any horizontal asymptotes.

What does an exponential growth curve show?

Exponential population growth: When resources are unlimited, populations exhibit exponential growth, resulting in a J-shaped curve. In logistic growth, population expansion decreases as resources become scarce. It levels off when the carrying capacity of the environment is reached, resulting in an S-shaped curve.

Which letter in the graph indicates a period of exponential growth?

Two types of population growth patterns may occur depending on specific environmental conditions: An exponential growth pattern (J curve) occurs in an ideal, unlimited environment. A logistic growth pattern (S curve) occurs when environmental pressures slow the rate of growth.

Which table represents an exponential function?

Answer: Table 2 represent the exponential function .