Matching Reflected Exponential Functions to Graphs

TLDR; Matching graphs of reflected exponential functions to equations based on sign changes is explained using the example of f(x) = e^x and its reflections across the x and y axes.

⚫️ Matching Graphs to Functions

The goal is to match each graph to the correct function based on the graph of f(x) = e^x.

To achieve this, the approach involves writing each equation in terms of f(x) = e^x.

By changing the sign of the inputs or x values in the original function, the function y = e^(-x) reflects the graph across the y-axis, producing graph 'A'.

🔴 Reflecting Across X-Axis

The equation y = -e^x is represented as y = -f(x), indicating a change in the sign of the function values or y values of the original function.

By changing the sign of the y values, the graph is reflected across the x-axis, resulting in graph 'B'.

🟢 Reflecting Across X and Y Axes

The equation y = -e^(-x) is expressed as y = -f(-x), indicating a change in the sign of the x values and the function values of the basic function f(x) = e^x.

By changing the sign of both the x and y values, the graph is reflected across both the x and y axes, giving us graph 'C'.