Attempt the problems below to self-assess topics that need attention. Use paper and pen or pencil and number each item so you may compare with the answers later. Do NOT use a calculator, graphing tool, or AI to assist you, unless otherwise indicated. Many of the topics may be reviewed in Chapter 8 below. Return to this pretest after you feel you have made sufficient progress. Answers may be found at the end of this chapter.
Sketch the graph of the base \(e\) exponential function, \(f(x) = e^x\text{,}\) and label at least three points on the graph including the \(y\)-intercept. State the domain and range of the graph and identify the equation of the horizontal asymptote. Then plot its inverse function’s graph \(f^{-1}(x)=\ln(x)\) on the same coordinate system. Label the corresponding points on the new curve, state its domain and range, and identify the equation of the vertical asymptote.
Discuss how the graph of \(y = 3\cdot 2^{-x} +4\) might be obtained from the graph of \(y=2^x\text{.}\) Then sketch the graph and label any relevant features. What’s the domain and range of the transformed graph?
