Questions: 3. Write the equation of the function whose parent function is f(x)=1/x and is stretched vertically by a factor of 5, reflected across the x-axis, shifted right 3 units, and shifted down 2 units. Sketch this graph and state the domain and range for the function. 4. Given the graph of the function below write the equation of the piecewise function f(x)= ii ii ii

3. Write the equation of the function whose parent function is f(x)=1/x and is stretched vertically by a factor of 5, reflected across the x-axis, shifted right 3 units, and shifted down 2 units. Sketch this graph and state the domain and range for the function.
4. Given the graph of the function below write the equation of the piecewise function
f(x)=

ii
ii
ii

Transcript text: 3. Write the equation of the function whose parent function is \(f(x)=\frac{1}{x}\) and is stretched vertically by a factor of 5, reflected across the \(x\)-axis, shifted right 3 units, and shifted down 2 units. Sketch this graph and state the domain and range for the function. 4. Given the graph of the function below write the equation of the piecewise function \[ f(x)=\left\{\begin{array}{l} i_{i} \\ i_{i} \\ i_{i} \end{array}\right. \]

Solution

Solution Steps

Step 1: Identify the Parent Function

The parent function given is \( f(x) = \frac{1}{x} \).

Step 2: Apply Vertical Stretch

The function is stretched vertically by a factor of 5. This modifies the function to \( f(x) = \frac{5}{x} \).

Step 3: Reflect Across the X-Axis

Reflecting the function across the x-axis changes the sign, resulting in \( f(x) = -\frac{5}{x} \).

Step 4: Shift Right 3 Units

Shifting the function right by 3 units modifies the function to \( f(x) = -\frac{5}{x-3} \).

Step 5: Shift Down 2 Units

Shifting the function down by 2 units results in \( f(x) = -\frac{5}{x-3} - 2 \).

Step 6: Sketch the Graph

To sketch the graph, plot the transformed function \( f(x) = -\frac{5}{x-3} - 2 \) on the coordinate plane.

Step 7: State the Domain and Range

Domain: All real numbers except \( x = 3 \) (since the function is undefined at \( x = 3 \)).
Range: All real numbers except \( y = -2 \) (since the horizontal asymptote is at \( y = -2 \)).