Questions: Determine where f is continuous. (Give your answer as an interval in the form (*,*). Use the symbol ∞ for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter ∅ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)

Solution Steps

The graph passes through the points $(0,0)$ and $(3,1)$. The slope is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$, so $m = \frac{1-0}{3-0} = \frac{1}{3}$.

The y-intercept is 0, so the equation of the line is $y = \frac{1}{3}x$. Since $f(x)$ represents $y$, we have $f(x) = \frac{1}{3}x$.

The function $f(x) = \frac{1}{3}x$ is a linear function, and linear functions are continuous everywhere. Therefore, the function is continuous on the interval $(-\infty, \infty)$.

Final Answer