$$ \leftarrow $$ Find the function that is finally graphed after the following transformations are applied to the graph of $$ y=\sqrt{x} $$ in the order listed. (1) Shift down 8 units (2) Rellect about the $$ x $$-axis (3) Reflect about the $$ y $$-axis

Question

UpStudy AI · Accepted Answer

To find the function that results from the given transformations applied to the graph of $$ y = \sqrt{x} $$, we will go through each transformation step by step.

1. **Shift down 8 units**: 
   - Shifting a function down by $$ k $$ units involves subtracting $$ k $$ from the function. 
   - For $$ y = \sqrt{x} $$, shifting down 8 units gives us:
   $$
   y = \sqrt{x} - 8
   $$

2. **Reflect about the $$ x $$-axis**: 
   - Reflecting a function about the $$ x $$-axis involves multiplying the entire function by -1.
   - Applying this to $$ y = \sqrt{x} - 8 $$ results in:
   $$
   y = -(\sqrt{x} - 8) = -\sqrt{x} + 8
   $$

3. **Reflect about the $$ y $$-axis**: 
   - Reflecting a function about the $$ y $$-axis involves replacing $$ x $$ with $$ -x $$ in the function.
   - Applying this to $$ y = -\sqrt{x} + 8 $$ gives us:
   $$
   y = -\sqrt{-x} + 8
   $$

Thus, the final function after applying all the transformations is:
$$
y = -\sqrt{-x} + 8
$$
The final function after the transformations is $$ y = -\sqrt{-x} + 8 $$.

Find the function that is finally graphed after the following transformations are applied to the
graph of in the order listed.
(1) Shift down 8 units
(2) Rellect about the -axis
(3) Reflect about the -axis

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Pre Calculus Questions

Find the function that is finally graphed after the following transformations are applied to the graph of in the order listed. (1) Shift down 8 units (2) Rellect about the -axis (3) Reflect about the -axis