A 100 -gallon fish tank fills at a rate of gallons per minute. The tank has already been filling for 5 minutes. The
function represents the remaining time in minutes needed to fill the tank. How is the graph of the paren
function transformed to create the graph of the function ?
It is a vertical stretch with a factor of 100 and a translation 5 units right.
It is a vertical stretch with a factor of 95 .
It is a vertical stretch with a factor of 100 and a translation 5 units down.
It is a vertical stretch with a factor of 500 .

Ask by Rodriguez Harris. in the United States

Jan 23,2025

Question

A 100 -gallon fish tank fills at a rate of gallons per minute. The tank has already been filling for 5 minutes. The
function represents the remaining time in minutes needed to fill the tank. How is the graph of the paren
function transformed to create the graph of the function ?
It is a vertical stretch with a factor of 100 and a translation 5 units right.
It is a vertical stretch with a factor of 95 .
It is a vertical stretch with a factor of 100 and a translation 5 units down.
It is a vertical stretch with a factor of 500 .

Ask by Rodriguez Harris. in the United States

Jan 23,2025

UpStudy AI · Accepted Answer

To transform the graph of the parent function $$ f(x) = \frac{1}{x} $$ to the function $$ f(x) = \frac{100}{x} - 5 $$, let's break down the modifications step by step:

1. **Vertical Stretch:**
   - The factor $$ 100 $$ multiplies the $$ \frac{1}{x} $$ term, which means the graph is vertically stretched by a factor of 100. This makes the graph steeper compared to the parent function.

2. **Vertical Translation (Shift):**
   - The term $$ -5 $$ subtracts 5 from the entire function, which translates the graph **5 units downward** along the y-axis.

Putting it all together, the transformation involves a vertical stretch by a factor of 100 followed by a downward shift of 5 units.

**Correct Transformation:**
- **Vertical stretch with a factor of 100 and a translation 5 units down.**

**Final Answer:**
It is a vertical stretch with a factor of 100 and a translation 5 units downward.
The graph of $$ f(x) = \frac{1}{x} $$ is vertically stretched by a factor of 100 and then translated 5 units downward to create the graph of $$ f(x) = \frac{100}{x} - 5 $$.

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