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

Solution Steps

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

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

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

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

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

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

• 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 \( y = -2 \)).

Final Answer