To use this applet, you should know that there are two graphs: one in red and one in blue, with matching functions in red and blue below the graphs. At the beginning, only one function appears because the two are identical.

- Use the slider below the graph to shift the blue graph to the right by 1 unit. How does the function change? What do you expect the graphs of
*y=sin(x+1.6)*and*y=sin(x-0.5)*will look like? - Re-center the function. Change the function to
*y=x²*by clicking on the top function in the column on the right, and then adjusting the exponent using the top slider. Again shift the blue graph to the right by 1 unit. How does the function change? What do you expect the graphs of*y=(x+1.6)²*and*y=(x-0.5)²*will look like? - Again re-center the function, and repeat questions 1 & 2 for the function
*y=*|*x*|. - Re-center the graph, and again choose the function
*y=sin(x)*. Use the slider to the left of the graph to shift the blue graph up 1 unit. How does the function change? What do you expect the graphs of*y=sin(x)+1.6*and*y=sin(x)-0.5*will look like? - Repeat question 4 for the functions
*y=x²*and*y=*|*x*|. - What do you expect the graph of
*y=sin(x+0.5)-2*to look like? Guess first, and use the applet to check your guess. - If you want to produce a parabola whose vertex is shifted to the left by 0.5 and down by 0.3, what might the function be?
- Again considering
*y=sin(x)*, what happens to the function if we vertically stretch (using the second slider from the top on the right) the graph by a factor of 1.5? What do you expect the graph of*y=(-0.5)sin(x) to look like? Guess first, then use the applet to check your guess.* - Predict the appearance of the graph of
*y=sin(2x)*. After writing your prediction, use the horizontal stretch slider (at top right) to produce the graph. Was your guess correct? - How do you expect the graph of
*y=(0.5 x)²*to be related to the graph of*y=x²*? Try it.