sketch the graph of a function that satisfies the conditions given below. f(0)=0, lim f(x)=0 as x→±∞, lim…

sketch the graph of a function that satisfies the conditions given below. f(0)=0, lim f(x)=0 as x→±∞, lim f(x)=lim f(x)=∞ as x→2⁻ and x→ - 2⁺, lim f(x)= - ∞ as x→2⁺ and x→ - 2⁻. choose the correct graph below.

sketch the graph of a function that satisfies the conditions given below. f(0)=0, lim f(x)=0 as x→±∞, lim f(x)=lim f(x)=∞ as x→2⁻ and x→ - 2⁺, lim f(x)= - ∞ as x→2⁺ and x→ - 2⁻. choose the correct graph below.

Answer

Explanation:

Step1: Analyze (f(0) = 0)

The function passes through the origin ((0,0)).

Step2: Analyze (\lim_{x\rightarrow\pm\infty}f(x)=0)

The function has a horizontal - asymptote (y = 0) as (x) approaches positive and negative infinity.

Step3: Analyze (\lim_{x\rightarrow2^{-}}f(x)=\lim_{x\rightarrow - 2^{+}}f(x)=\infty)

The function has vertical asymptotes at (x = 2) and (x=-2), and the function approaches positive infinity as (x) approaches (2) from the left and ( - 2) from the right.

Step4: Analyze (\lim_{x\rightarrow2^{+}}f(x)=\lim_{x\rightarrow - 2^{-}}f(x)=-\infty)

The function approaches negative infinity as (x) approaches (2) from the right and ( - 2) from the left.

Answer:

A. Option Text (assuming the graph in option A satisfies all the above - mentioned conditions based on the analysis of limits and the point ((0,0)))