Graphs of Exponential Functions in the form of \(y = ka^{x}\)

Relationship among Graphs of Exponential Functions with Different Bases

Graphs of Logarithmic Functions in the form of \(y = k \log_{a} x\)

Relationship among Graphs of Logarithmic Functions with Different Bases

For logarithmic functions in the form of \(y = \log_{a} x\) :<ul><li>When \(a &gt; 1\) , the curve is closer to the axes with greater value of \(a\) .</li><li>When \(0 &lt; a &lt; 1\) , the curve is closer to the axes with smaller value of \(a\) .</li><li>They all pass through the point \((1, 0)\) .</li><li>They all have a vertical asymptote as the \(y\) -axis.</li></ul>

Relationship between Graphs of Exponential and Logarithmic Functions with the Same Base

For exponential and logarithmic functions in the forms of \(y = a^x\) and \(y = \log_a x\) :<ul><li>Their graphs are symmetrical about the straight line \(y = x\).</li><li>The functions \(y = a^x\) and \(y = \log_a x\) are the inverse functions of each other.</li></ul>