Exponential Transformations

Front

What is reflection in exponential transformations?

Back

Reflection refers to flipping a graph over a specific axis. In exponential transformations, reflection over the x-axis changes the sign of the function's output.

Front

What does a stretch of 5 mean in exponential transformations?

Back

A stretch of 5 means that the graph of the function is vertically stretched by a factor of 5, making it taller without changing its horizontal position.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input (x) approaches positive or negative infinity.

Front

What is the horizontal asymptote of the function f(x) = e^x + 6?

Back

The horizontal asymptote is y = 6.

Front

What does a vertical shift of 'up 6' indicate?

Back

A vertical shift of 'up 6' means that every point on the graph of the function is moved 6 units higher on the y-axis.

Front

What is the effect of a vertical compression in exponential transformations?

Back

A vertical compression reduces the height of the graph, making it flatter, and is represented by a factor less than 1.

Front

How does a horizontal shift to the right affect the graph of an exponential function?

Back

A horizontal shift to the right means that the entire graph moves to the right by a specified number of units, affecting the function's input.

Front

What is the general form of an exponential decay equation?

Back

The general form of an exponential decay equation is f(x) = a * e^(-bx) where a > 0 and b > 0.

Front

What does it mean for an exponential function to be shifted 1 unit right and 3 units down?

Back

This means the function is transformed to f(x) = a * e^(-b(x-1)) - 3.

Front

What is the significance of the base 'e' in exponential functions?

Back

The base 'e' (approximately 2.718) is a mathematical constant that is the base of natural logarithms and is used in continuous growth or decay models.