3. Given: $$ f(x)=\left(\frac{1}{4}\right)^{x} $$ Describe the transformation: 4. Given: $$ f(x)=\left(\frac{1}{4}\right)^{x} $$ Describe the transformation: Transformation: $$ g(x)=\left(\frac{1}{4}\right)^{x}-3 $$ 5. Given: $$ f(x)=\left(\frac{1}{4}\right)^{x} $$ Describe the transformation:

Question

UpStudy AI · Accepted Answer

To describe the transformations of the function $$ f(x) = \left(\frac{1}{4}\right)^{x} $$, we will analyze the changes made to the function in each case.

### 3. Transformation of $$ f(x) = \left(\frac{1}{4}\right)^{x} $$

The function $$ f(x) = \left(\frac{1}{4}\right)^{x} $$ is an exponential decay function. The base $$ \frac{1}{4} $$ is less than 1, which means that as $$ x $$ increases, $$ f(x) $$ decreases towards 0.

### 4. Transformation: $$ g(x) = \left(\frac{1}{4}\right)^{x} - 3 $$

In this case, the transformation from $$ f(x) $$ to $$ g(x) $$ involves a vertical shift.

- **Vertical Shift Downward**: The function $$ g(x) = f(x) - 3 $$ indicates that the entire graph of $$ f(x) $$ is shifted downward by 3 units.

This means that every point on the graph of $$ f(x) $$ is moved down 3 units. For example, if $$ f(0) = 1 $$, then $$ g(0) = 1 - 3 = -2 $$.

### 5. General Description of Transformation

If we consider a general transformation of the form $$ g(x) = f(x) + k $$, where $$ k $$ is a constant:

- If $$ k > 0 $$, the graph of $$ f(x) $$ shifts upward by $$ k $$ units.
- If $$ k < 0 $$, the graph of $$ f(x) $$ shifts downward by $$ |k| $$ units.

In the specific case of $$ g(x) = \left(\frac{1}{4}\right)^{x} - 3 $$, we have $$ k = -3 $$, indicating a downward shift of 3 units.

In summary, the transformation from $$ f(x) $$ to $$ g(x) $$ is a vertical shift downward by 3 units.
The function $$ f(x) = \left(\frac{1}{4}\right)^{x} $$ is an exponential decay function. - **Transformation 4**: The function $$ g(x) = \left(\frac{1}{4}\right)^{x} - 3 $$ shifts the graph of $$ f(x) $$ downward by 3 units. In summary, the transformation involves a vertical shift downward by 3 units.

Given:
Describe the transformation:

Given:
Describe the transformation: Transformation:

Given:
Describe the transformation:

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Pre Calculus Questions

Given: Describe the transformation: Given: Describe the transformation: Transformation: Given: Describe the transformation: