Question

Identify any vertical, horizontal, or oblique asymptotes in the graph of y=ƒ(x). State the domain of ƒ.

Accepted Answer

Step 1: Identify the vertical asymptote by looking for the vertical line where the graph approaches infinity or negative infinity. In the graph, the red curve approaches a vertical dashed line at $$x = -2$$, indicating a vertical asymptote there. Step 2: Identify the horizontal asymptote by checking if the graph approaches a constant value as $$x$$ goes to positive or negative infinity. In this graph, there is no horizontal line that the curve approaches, so there is no horizontal asymptote. Step 3: Identify the oblique (slant) asymptote by observing if the graph approaches a non-horizontal, non-vertical line as $$x$$ goes to infinity or negative infinity. The green dashed line with positive slope is the oblique asymptote, which appears to be $$y = x - 2. $$Step 4: State the domain of the function $$f. $$Since there is a vertical asymptote at $$x = -2$$, the function is undefined there. Therefore, the domain is all real numbers except $$x = -2$$, which can be written as $$(-\infty, -2) \cup (-2, \infty). $$Step 5: Summarize the asymptotes and domain: Vertical asymptote at $$x = -2$$, oblique asymptote at $$y = x - 2$$, no horizontal asymptote, and domain $$(-\infty, -2) \cup (-2, \infty).$$

Identify any vertical, horizontal, or oblique asymptotes in the graph of y=ƒ(x). State the domain of ƒ.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Vertical Asymptotes

Horizontal and Oblique Asymptotes

Domain of a Function