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 observing where the graph approaches a vertical line but never crosses it. In the graph, the vertical asymptote is at $$x = 7$$, indicated by the dashed blue vertical line. Step 2: Identify the horizontal asymptote by looking for a horizontal line that the graph approaches as $$x$$ goes to positive or negative infinity. The graph approaches the horizontal line $$y = 6 ($$green dashed line) as $$x$$ goes to both positive and negative infinity. Step 3: Check for any oblique (slant) asymptotes by seeing if the graph approaches a non-horizontal, non-vertical line as $$x$$ goes to infinity. In this graph, there is no oblique asymptote since the graph approaches a horizontal line instead. Step 4: State the domain of the function $$f. $$Since there is a vertical asymptote at $$x = 7$$, the function is undefined at this point. Therefore, the domain is all real numbers except $$x = 7$$, which can be written as $$(-\infty, 7) \cup (7, \infty). $$Step 5: Summarize the asymptotes and domain: Vertical asymptote at $$x = 7$$, horizontal asymptote at $$y = 6$$, no oblique asymptote, and domain $$(-\infty, 7) \cup (7, \infty).$$

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