Write a formula for $$ f(x)=\frac{1}{x^{2}} $$ shifted up 2 units and left 4 units.

Question

UpStudy AI · Accepted Answer

Below is the step-by-step process to find the new function:

1. **Original Function:**  
   We start with  
   $$
   f(x) = \frac{1}{x^2}.
   $$

2. **Shift Left by 4 Units:**  
   To shift the graph left by 4 units, replace $$ x $$ with $$ x+4 $$. This yields:  
   $$
   f(x+4) = \frac{1}{(x+4)^2}.
   $$

3. **Shift Up by 2 Units:**  
   To move the graph up by 2 units, add 2 to the function:  
   $$
   \frac{1}{(x+4)^2} + 2.
   $$

4. **Final Transformed Function:**  
   The new function is:  
   $$
   g(x) = \frac{1}{(x+4)^2} + 2.
   $$

Thus, the formula for $$ f(x)=\frac{1}{x^2} $$ shifted up 2 units and left 4 units is  
$$
\boxed{g(x) = \frac{1}{(x+4)^2} + 2}.
$$
The transformed function is $$ g(x) = \frac{1}{(x+4)^2} + 2 $$.

Write a formula for shifted up 2 units and left 4 units.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Pre Calculus Questions