Question

which of the following is the graph of the function $y = x^3$?

Explanation:

Step1: Identify function type

The function $y=e^x$ is an exponential growth function.

Step2: Key properties of $y=e^x$

1. When $x=0$, $y=e^0=1$, so it passes through $(0,1)$.
2. As $x\to+\infty$, $y\to+\infty$ (grows rapidly).
3. As $x\to-\infty$, $y\to0$ (approaches x-axis from above).
4. The function is always positive, never crosses the x-axis.

Step3: Match to graphs

• Top graph: Passes through $(0,1)$, grows rapidly for positive $x$, approaches x-axis for negative $x$ (matches all properties).
• Middle graph: Grows very slowly, does not match exponential growth rate.
• Bottom graph: Is a parabola (quadratic function), not exponential.

Answer:

The first (top) graph