Question

how can you use transformations to graph this function?

\\y = 3 \cdot 7^{-x} + 2\\

explain your steps.

Explanation:

Identify the parent function

Using the Exponential Function Graphs knowledge point

$$ y = 7^x $$

Apply horizontal reflection

Using the Exponential Function Transformations knowledge point

$$ y = 7^{-x} $$

Apply vertical dilation

Using the Exponential Function Transformations knowledge point

$$ y = 3 \cdot 7^{-x} $$

Apply vertical translation

Using the Exponential Function Transformations knowledge point

$$ y = 3 \cdot 7^{-x} + 2 $$

Answer:

To graph the function \(y = 3 \cdot 7^{-x} + 2\) using transformations, start with the parent function \(y = 7^x\) and apply the following steps:

1. Reflect horizontally across the y-axis to get \(y = 7^{-x}\).
2. Stretch vertically by a factor of 3 to get \(y = 3 \cdot 7^{-x}\).
3. Shift vertically up by 2 units to get \(y = 3 \cdot 7^{-x} + 2\).