? Question Each statement describes a transformation of the graph of $$ f(x)=x $$. Which statement correctly describes the graph of $$ g(x) $$ if $$ g(x)=f(x)+7 $$ ? O It is the graph of $$ f(x) $$ translated 7 units down. O It is the graph of $$ f(x) $$ translated 7 units to the right. O It is the graph of $$ f(x) $$ where the slope is decreased by 7 . $$ f(x) $$ translated 7 units up.

Question

UpStudy AI · Accepted Answer

When you transform the function $$ f(x) $$ to $$ g(x) = f(x) + 7 $$, you are adding 7 to every output value of $$ f(x) $$. This operation results in shifting the entire graph of $$ f(x) $$ **vertically**.

Here's a breakdown of what each option represents:

1. **7 units down:** This would correspond to $$ g(x) = f(x) - 7 $$, not $$ f(x) + 7 $$.
2. **7 units to the right:** This would involve a horizontal shift, such as $$ g(x) = f(x - 7) $$.
3. **Slope decreased by 7:** Changing the slope would involve multiplying $$ f(x) $$ by a factor, not adding a constant.
4. **7 units up:** Adding 7 to $$ f(x) $$ shifts the graph upward by 7 units.

**Correct Answer:**
• It is the graph of $$ f(x) $$ translated 7 units up.
The graph of $$ g(x) = f(x) + 7 $$ is the graph of $$ f(x) $$ translated 7 units up.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Pre Algebra Questions