Exponential Transformations

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b^x), where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent. It shows rapid growth or decay.

Front

What characterizes exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to a rapid increase over time.

Front

What characterizes exponential decay?

Back

Exponential decay occurs when the decrease rate of a value is proportional to its current value, leading to a rapid decrease over time.

Front

How does the graph of y = a(b^x) behave when b > 1?

Back

The graph of y = a(b^x) with b > 1 shows exponential growth, rising steeply as x increases.

Front

How does the graph of y = a(b^x) behave when 0 < b < 1?

Back

The graph of y = a(b^x) with 0 < b < 1 shows exponential decay, falling steeply as x increases.

Front

What is a vertical translation in the context of function transformations?

Back

A vertical translation shifts the graph of a function up or down without changing its shape.

Front

What is a horizontal translation in the context of function transformations?

Back

A horizontal translation shifts the graph of a function left or right without changing its shape.

Front

What does the transformation y = f(x - 3) represent?

Back

The transformation y = f(x - 3) represents a horizontal translation of the function f(x) to the right by 3 units.

Front

What does the transformation y = f(x) + 2 represent?

Back

The transformation y = f(x) + 2 represents a vertical translation of the function f(x) upward by 2 units.

Front

What is the effect of a negative sign in front of an exponential function, such as y = -2^x?

Back

A negative sign in front of an exponential function reflects the graph across the x-axis.