Attributes and Transformations of Exponential Functions

Front

What is the horizontal line that an exponential function approaches but never touches?

Back

Asymptote

Front

What is the equation of the asymptote of the graph of an exponential function?

Back

y=0

Front

What type of function describes a situation where the value increases rapidly?

Back

Exponential Growth

Front

What equation would yield a transformation right 3 units if your initial function was y=2^x?

Back

y=2^(x-3)

Front

How does adding a constant 'k' in the equation y=a(b)^x+k transform the parent function?

Back

Vertical Translation

Front

What is the growth factor in an exponential function?

Back

The constant factor by which the function's value increases for each unit increase in x.

Front

What is the general form of an exponential function?

Back

y = a(b)^x, where a is a constant and b is the base.

Front

What does a negative growth factor indicate in an exponential function?

Back

Exponential Decay

Front

How does the base 'b' affect the growth of an exponential function?

Back

If b > 1, the function exhibits exponential growth; if 0 < b < 1, it exhibits exponential decay.

Front

What is the effect of a vertical stretch on an exponential function?

Back

It increases the steepness of the graph.