To get a better feeling for the effect of \(a\) and \(b\) on the graph, examine the sets of graphs below. We can also see from the graph the long run behavior: as \( x\to\infty \), \( f(x)\to 0 \), and as \( x\to -\infty \), \( f(x)\to \infty \). Since \(a \gt 0\), the graph will be concave up. Since \(b \lt 1\), the graph will be decreasing towards zero. A graph obtained from \(y=a^x\) by dilations, reflections in the axes and translations also has no critical points.\right) \). If \(a>0\), the translation is to the right, and if \(a0\), the translation is upwards, and if \(a0\) with \(a \neq 1\), the function \(y=a^x\) has no critical points: the derivative \(\dfrac = \log_e a \cdot a^x\) is never 0.
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