Questions: q(x) = 7/(3x^3) if x < 1 -5/3 x if x > 1 Step 1 of 3: Identify the general shape and direction of the graph of this function on the interval (-∞, 1).

Solution Steps

We are asked to identify the shape of the graph of $q(x)$ on the interval $(-\infty, 1)$. On this interval, the function is defined as $q(x) = \frac{7}{3x^3}$.

The function $\frac{7}{3x^3}$ resembles the function $\frac{1}{x^3}$. When $x$ approaches 0 from the left, the function approaches $-\infty$. As $x$ goes to $-\infty$, the function approaches 0. The function is always negative for negative $x$ values.

The second graph is the correct option, as it depicts a portion of a curve that is asymptotic to the y-axis as x approaches zero from the left and asymptotic to the x-axis as x approaches $-\infty$.

Final Answer: The second graph.