### Exponential functions and their graphs

Question Sample Titled 'Exponential functions and their graphs'

A function in the form ${f{{\left({x}\right)}}}={k}{a}^{{x}}$ , where ${a}>{0}$, ${a}\ne{1}$ and ${k}\ne{0}$ , is called an exponential function.
Range of ${a}$${a}\gt{1}$${0}\lt{a}\lt{1}$
Graph of ${y}={a}^{{x}}$
Common characteristics1. The graph cuts the y-axis at ${\left({0},{1}\right)}$. 2. The graph lies above the x-axis. 3. The graph has neither a maximum point, a minimum point nor an axis of symmetry.
Differences1. The value of ${a}^{{x}}$ increases as ${a}$ increases. 2. The value of ${a}^{{x}}$gets closer and closer to zero as ${a}$ decreases indefinitely. 3. As ${x}$ increases, the rate of increase of ${a}^{{x}}$ increases.1. The value of ${a}^{{x}}$decreases as ${x}$ increases. 2. The value of ${a}^{{x}}$gets closer and closer to zero as ${x}$ increases indefinitely. 3. As ${x}$ increases, the rate of decrease of ${a}^{{x}}$ decreases.
Note: The graph of ${y}={a}^{{x}}$ and ${y}={\left(\dfrac{{1}}{{a}}\right)}^{{x}}$ have reflectional symmetry about the y-axis.

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