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Graphing functions of the form y = Af(B(x-C))+D

Drag the dots to set the parameters A, B, C, D & the type of function you wish to see.

Drag the dot labeled “x” to trace the curve.

Click the buttons to show or hide the curve & to show or hide the equation (parameters & type).

Questions

1. A, B, C, & D have specific affects on the shape of the "parent" function. Graph y = -(x+1)^2 - 2 & explain exactly how A,C, & D affect the graph. Confirm your theory using y = -e^(x+1) - 2.

2. Hide the graph. Adjust the function type and parametere to graph y = 3/(x+1) - .5. Do you know what the graph looks like? click show graph to check you answer. Repeat with other parent graphs and transformations. Can you come up with an equation (of the form y = Af(B(x-C)) + D) whose graph is difficult to guess?

3. Reload the web page. Click on Hide Equation. Drag the function type dot. Do you recognize each graph? Click on show equation if you need a reminder.

4. Reload the web page & click hide equation. Adjust the function type, and the parameters A, C, & D (leave B alone). Can you make a reasonable guess for the equation of the graph? Click show equation to check your guess. Can you come up with a graph whose equation is hard to guess?

5. How does the factor B affect the graph. What happens if B is negative? Is y = ln(2x - 4) the same as y = ln(2(x-4))?