The function $$ h $$ is defined as follows. $$ h(x)=x^{2}-1 $$ If the graph of $$ h $$ is translated vertically, downward by 3 units, it becomes the graph of a function $$ f $$, Find the expression for $$ f(x) $$. Note that the ALEKS graphing calculator may be helpful in checking your answer, $$ f(x)=\square $$

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To find the expression for the function $$ f(x) $$ after translating the graph of $$ h(x) $$ vertically downward by 3 units, we can follow these steps:

1. **Identify the original function**: The original function is given as:
   $$
   h(x) = x^2 - 1
   $$

2. **Understand the translation**: A vertical translation downward by $$ k $$ units means we subtract $$ k $$ from the function. In this case, $$ k = 3 $$.

3. **Apply the translation**: To find the new function $$ f(x) $$, we subtract 3 from $$ h(x) $$:
   $$
   f(x) = h(x) - 3
   $$

4. **Substitute $$ h(x) $$**:
   $$
   f(x) = (x^2 - 1) - 3
   $$

5. **Simplify the expression**:
   $$
   f(x) = x^2 - 1 - 3 = x^2 - 4
   $$

Thus, the expression for $$ f(x) $$ is:
$$
f(x) = x^2 - 4
$$

So, the final answer is:
$$
f(x) = x^2 - 4
$$
$$ f(x) = x^2 - 4 $$

The function is defined as follows.

If the graph of is translated vertically, downward by 3 units, it becomes the graph of a function ,
Find the expression for .
Note that the ALEKS graphing calculator may be helpful in checking your answer,

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The function is defined as follows. If the graph of is translated vertically, downward by 3 units, it becomes the graph of a function , Find the expression for . Note that the ALEKS graphing calculator may be helpful in checking your answer,