Graphs Transformations of Exponential Functions

Front

What is the general form of an exponential function?

Back

y = a * b^x, where a is a constant, b is the base, and x is the exponent.

Front

What does it mean to translate a graph right by 3 units?

Back

The function is modified by subtracting 3 from the x-value: f(x) becomes f(x-3).

Front

How do you translate the function g(x) = (1/2)^x 5 units left?

Back

The new function is f(x) = (1/2)^(x+5).

Front

What is the effect of adding a constant to an exponential function?

Back

Adding a constant shifts the graph vertically. For example, f(x) = (1/2)^x + 4 shifts the graph up by 4 units.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base (b) is greater than 1, while exponential decay occurs when the base (b) is between 0 and 1.

Front

What transformation occurs in the function y = 2^(x-3)?

Back

This function is translated right by 3 units.

Front

What does the term 'vertical stretch' mean in the context of exponential functions?

Back

A vertical stretch occurs when the value of 'a' in y = a * b^x is greater than 1, making the graph steeper.

Front

What is the effect of a negative exponent in an exponential function?

Back

A negative exponent indicates a reciprocal: for example, (1/2)^-x = 2^x.

Front

How do you determine if a graph represents exponential growth or decay?

Back

If the graph rises as x increases, it represents growth; if it falls, it represents decay.

Front

What is the transformation for the function y = 3 * 2^(x-1) + 2?

Back

This function is stretched vertically by a factor of 3, translated right by 1 unit, and shifted up by 2 units.