Day 1 Exponential Transformations

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What does vertical translation mean in the context of exponential functions?

Back

Vertical translation refers to shifting the graph of the function up or down along the y-axis. For example, f(x) = b^x + k translates the graph k units vertically.

Front

What does horizontal translation mean in the context of exponential functions?

Back

Horizontal translation refers to shifting the graph of the function left or right along the x-axis. For example, f(x) = b^(x - h) translates the graph h units to the right.

Front

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

Back

Adding a positive constant to an exponential function results in a vertical translation of the graph upwards.

Front

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

Back

Adding a negative constant to an exponential function results in a vertical translation of the graph downwards.

Front

What is the general form of an exponential function with a horizontal translation?

Back

The general form is f(x) = a * b^(x - h), where h represents the horizontal translation.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is the line that the graph approaches as x approaches positive or negative infinity. For functions of the form f(x) = a * b^x + k, the horizontal asymptote is y = k.

Front

How do you determine the vertical translation of an exponential function?

Back

The vertical translation can be determined by the constant added or subtracted from the function. For example, in f(x) = b^x + k, the graph is translated k units vertically.

Front

What is the transformation of the function f(x) = 3^(x) + 2?

Back

The transformation is a vertical translation up 2 units.

Front

What is the transformation of the function f(x) = 3^(x - 1)?

Back

The transformation is a horizontal translation right 1 unit.