Question

sketch a possible graph of a function that satisfies the conditions below. f(0)=2, lim x→0⁻ f(x)= - 2, lim x→0⁺ f(x)=2. choose the correct graph below. a. graph image. b. graph image. c. graph image. d. graph image.

Explanation:

Step1: Analyze the function - value at \(x = 0\)

The value of the function \(f(0)=2\) means the graph has a point \((0,2)\) (a solid - dot since \(f(0)\) is defined as 2).

Step2: Analyze the left - hand limit

The left - hand limit \(\lim_{x
ightarrow0^{-}}f(x)= - 2\). This means as \(x\) approaches 0 from the left, the function approaches \(y=-2\). There should be an open - dot at \((0, - 2)\) on the left - hand side of \(x = 0\).

Step3: Analyze the right - hand limit

The right - hand limit \(\lim_{x
ightarrow0^{+}}f(x)=2\). This means as \(x\) approaches 0 from the right, the function approaches \(y = 2\). There should be an open - dot at \((0,2)\) on the right - hand side of \(x = 0\) (but since \(f(0)=2\), the solid dot at \((0,2)\) takes precedence for the right - hand side).

Answer:

A.