Matching Exponential Function Graphs with Shifted Equations

TLDR; Matching translated exponential function graphs to equations based on shifts up, down, left, or right from the basic function.

📈 Matching Graphs to Functions

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

Four other graphs are shifts up, down, left, or right from the basic function, and the task is to write each function in terms of f(x).

The value of c determines if the graph has shifted left or right, while the value of d determines whether the graph has shifted up or down.

If c is positive, the graph has shifted left, and if c is negative, the graph has shifted right.

Similarly, if d is positive, the graph has shifted up, and if d is negative, the graph has shifted down.

📊 Function: e^(x + 2)

The first function is e raised to the power of x + 2, which implies the input into f would be the quantity x + 2.

This can be written as y = f(x + 2), and in this form, it's recognized that c would be +2, indicating a shift left two units.

Observing the graphs, the blue graph is two units left of the black graph, hence producing graph 'A'.

📈 Function: e^(x) + 2

The function e to the x + 2 is written as y = e to the x is f(x) and then + 2, indicating that d is +2, resulting in a shift up two units.

The red graph has been shifted two units up from the black graph, leading to the production of graph 'B'.

📊 Function: e^(x - 2)

In this case, the exponent is x - 2, so the function is written as y = f(x - 2), signifying that c is -2, causing the graph to be shifted right two units.

The purple graph is two units right of the black graph, resulting in the production of graph 'D'.

📈 Function: e^(x) - 2

The function y = f(x - 2) indicates that d is -2, leading to a shift down two units, producing the green graph or graph 'C'.