1. The problem is to understand the shape and behavior of the function $f(x) = a^x$ where $a > 0$ and $a \neq 1$. 2. The formula for an exponential function is $f(x) = a^x$, where $a$ is the base and $x$ is the exponent. 3. Important rules: - If $a > 1$, the function is increasing and passes through the point $(0,1)$. - If $0 < a < 1$, the function is decreasing and also passes through $(0,1)$. - The function never touches the x-axis but approaches it asymptotically as $x \to -\infty$ if $a > 1$, or as $x \to \infty$ if $0 < a < 1$. 4. The graph passes near the point $(0,1)$ because $a^0 = 1$ for any valid $a$. 5. For the case described (graph decreases steeply for negative $x$ and approaches the x-axis asymptotically as $x$ increases positively), this corresponds to $0 < a < 1$. 6. Therefore, the function is a decreasing exponential function with horizontal asymptote $y=0$. Final answer: The graph of $f(x) = a^x$ with $0 < a < 1$ is a decreasing curve passing through $(0,1)$ and approaching the x-axis asymptotically as $x \to \infty$.