show instructions question 34 (1 point) use the graph to find the interval(s) for which the function is…

show instructions question 34 (1 point) use the graph to find the interval(s) for which the function is continuous. f(x)=x²/(x² + 1) -2 2 a 0,1 b (-∞, 0) and (0,∞) c (-∞,∞) d 0,1) e none of these

show instructions question 34 (1 point) use the graph to find the interval(s) for which the function is continuous. f(x)=x²/(x² + 1) -2 2 a 0,1 b (-∞, 0) and (0,∞) c (-∞,∞) d 0,1) e none of these

Answer

Explanation:

Step1: Recall continuity condition

A rational - function $y = \frac{p(x)}{q(x)}$ is continuous everywhere except where $q(x)=0$. For the function $f(x)=\frac{x^{2}}{x^{2}+1}$, the denominator is $q(x)=x^{2}+1$.

Step2: Find when denominator is zero

Set $x^{2}+1 = 0$. Then $x^{2}=-1$. Since the square of any real number $x\in R$ satisfies $x^{2}\geq0$, there are no real - valued solutions for $x$ such that $x^{2}=-1$. So the function $f(x)=\frac{x^{2}}{x^{2}+1}$ is continuous for all real numbers.

Answer:

C. $(-\infty,\infty)$