All AP Courses

Lab

Function Grapher

The dashed curve is a parent function f. The colored curve is g(x) = a f(b(x + c)) + d. Before you move a slider, say which way you expect the graph to move or stretch, then check.

Challenges

  1. With the polynomial family, set c to 3. Which way does the vertex move, and why is it the opposite of the sign of c?
  2. With the rational family, move the vertical asymptote to x = −2 and the horizontal asymptote to y = 4. Which two sliders did you need?
  3. With the sinusoidal family, make the period 4π without changing the amplitude. What value of b does that take?
  4. With the exponential family, make b negative. Which end of the graph now approaches the horizontal asymptote?
  5. With the logarithmic family and a = 1, set b to 2. Now set b back to 1 and find the value of d that gives the same graph. Which property of logarithms explains it?

Topics this lab supports