Chapter 6 - Inverse Functions - 6.2 Exponential Functions and Their Derivatives - 6.2 Exercises - Page 418: 5

We observe from the above graph that: I. The curves for functions $y=3^{x},y=10^{x}$ are rapidly increasing. II. The curves for functions $y=(\frac{1}{3})^{x},y=(\frac{1}{10})^{x}$ are decreasing. III. All curves of these function passes through the points $(0, 1)$. IV. The rate of the function $y=10^{x}$ is more than that of $y=3^{x}$ reason being $10 > 3$. V. The curve $y=(\frac{1}{3})^{x}$ is the reflected image of the curve $y=3^{x}$ about Y-axis. VI. The curve $y=(\frac{1}{10})^{x}$ is the reflected image of the curve $y=10^{x}$ about Y-axis. VII. All of these functions represented by graphs approach to 0 as ${0 \to \infty}$ . The graph is depicted as follows: We observe from the above graph that: I. The curves for functions $y=3^{x},y=10^{x}$ are rapidly increasing. II. The curves for functions $y=(\frac{1}{3})^{x},y=(\frac{1}{10})^{x}$ are decreasing. III. All curves of these function passes through the points $(0, 1)$. IV. The rate of the function $y=10^{x}$ is more than that of $y=3^{x}$ reason being $10 > 3$. V. The curve $y=(\frac{1}{3})^{x}$ is the reflected image of the curve $y=3^{x}$ about Y-axis. VI. The curve $y=(\frac{1}{10})^{x}$ is the reflected image of the curve $y=10^{x}$ about Y-axis. VII. All of these functions represented by graphs approach to 0 as ${0 \to \infty}$ . The graph is depicted as follows: 