Questions: What transformations are needed to go from the graph of the basic function f(x)=1/x to the graph of g(x)=1/(x-1)+19 Shift right 1 units, and shift down 19 units Shift left 19 units, and shift up 1 units Shift right 1 units, and shift up 19 units. Shift left 1 units, and shift up 19 units. Shift up 1 units. None of the above

Solution Steps

To determine the transformations needed to go from the graph of \( f(x) = \frac{1}{x} \) to the graph of \( g(x) = \frac{1}{x-1} + 19 \):

1. Identify the horizontal shift: The term \( x-1 \) inside the function indicates a shift to the right by 1 unit.
2. Identify the vertical shift: The term \( +19 \) outside the function indicates a shift upwards by 19 units.

Thus, the correct transformation is to shift the graph of \( f(x) \) right by 1 unit and up by 19 units.

No Python code is needed for this transformation identification.### Step 1: Identify the Basic Function The basic function given is: \[ f(x) = \frac{1}{x} \]

The transformed function is: \[ g(x) = \frac{1}{x-1} + 19 \]

The term \( x-1 \) inside the function \( \frac{1}{x-1} \) indicates a horizontal shift. Specifically, \( x-1 \) means the graph of \( f(x) \) is shifted to the right by 1 unit.

The term \( +19 \) outside the function \( \frac{1}{x-1} \) indicates a vertical shift. Specifically, \( +19 \) means the graph of \( f(x) \) is shifted up by 19 units.

Final Answer