Change the position of the slider in order to change the base [b][i]a[/i][/b] which is used as the base of the exponential and the logarithmic functions.
Recall the properties of an exponential graph. Select all that apply for [math]y=a^x[/math] where [math]a>1[/math]
Notice the properties of the logarithmic graph. Select all that apply for [math]y=log_ax[/math] where [math]a>1[/math]
What is the relationship between points D and B?
The x-coordinate and the y-coordinate exchange places.
How do the properties of the two function types relate? Select all that apply.
How do the properties of the two function types differ? Select all that apply.
What do you notice about the intersection between the exponential and logarithmic graphs when they have the same base?
What is the slope and y-intercept of the line y=x? Select multiple answers.
If you shift an exponential function horizontally or vertically, how would this transformation apply to its corresponding logarithmic equation? Talk about it with your partner and make a prediction.
Did your conjecture hold true? Explain.
Fill in the blanks below:When the bases are the same, a [b][u]horizontal [/u][/b]translation of an exponential function corresponds to a ___________ translation of its corresponding logarithmic function.[br]When the bases are the same, a [b][u]vertical [/u][/b]translation of an exponential function corresponds to a ___________ translation of its corresponding logarithmic function.