In class we looked at functions of the form \(f(x)=a\cdot b^x+d\), and we had a brief discussion of the effect of the values of \(a, b,\) and \(c\) on the graph of the function. Below, you’ll extend this treatment to understand the effect of the values of \(a, b, c,\) and \(d\) on the graph of functions of the form \(f(x)=a\cdot b^{x-c}+d\).
Read through Investigation 1 on page 95 of the textbook, and use graphing software (I suggest either GeoGebra or Desmos) to explore the effects of various values on the graph of each function. As discussed in class, using sliders can make it easier to see the effect of each, and you can see an example of this below. (But it’s more fun to try to make your own version of this!)
Once you’ve completed your investigation, complete questions 4 and 5 from Exercise 3F. (Record your answers in your notebook, and then bring your notebook to class!)