Find the Asymptotes y = square root of x

Problem

y=√(,x)

Solution

1. Identify the domain of the function. Since the square root is only defined for non-negative values in the real number system, the domain is x≥0

2. Check for vertical asymptotes by looking for values of x where the function approaches infinity. As x approaches 0 from the right, y approaches 0 There are no values of x that cause the function to go to infinity; therefore, there are no vertical asymptotes.

3. Check for horizontal asymptotes by evaluating the limit of the function as x approaches infinity.

(lim_x→∞)(√(,x))=∞

Since the limit does not result in a finite constant, there are no horizontal asymptotes.

4. Check for oblique (slant) asymptotes by evaluating the limit of y/x as x approaches infinity.

(lim_x→∞)(√(,x)/x)=(lim_x→∞)(1/√(,x))=0

While the slope m is 0 the limit (lim_x→∞)(ƒ(x)−m*x) results in ∞ so no oblique asymptote exists.

Final Answer

y=√(,x)* has no asymptotes

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