Subjects algebra

Rational Function Fcd8D9

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1. **State the problem:** We are given the function $$y = -\frac{1}{x+2}$$ and a set of points plotted on its graph. We need to verify if the point at $x=1$ is correct. 2. **Recall the function and asymptotes:** The function is a rational function with a vertical asymptote where the denominator is zero, i.e., at $$x+2=0 \Rightarrow x=-2$$. The horizontal asymptote is $$y=0$$ because as $$x \to \pm \infty$$, $$y \to 0$$. 3. **Evaluate the function at $x=1$:** Substitute $x=1$ into the function: $$y = -\frac{1}{1+2} = -\frac{1}{3} \approx -0.33$$ 4. **Compare with the plotted point:** The plotted point at $x=1$ is $(1, 0.33)$, which is positive. However, the function value is approximately $-0.33$, which is negative. 5. **Conclusion:** The point $(1, 0.33)$ is incorrect for the function $$y = -\frac{1}{x+2}$$. The correct point should be $(1, -0.33)$. This confirms the error in the plotted graph at $x=1$.