Questions: y = x - 1 + 5 What shifts have occurred? right 1, down 5 left 1, down 5 left 1, up 5 right 1, up 5

Solution Steps

To determine the shifts that have occurred in the function \( y = |x - 1| + 5 \), we need to analyze the transformations applied to the basic absolute value function \( y = |x| \). The expression \( |x - 1| \) indicates a horizontal shift to the right by 1 unit, and the \( +5 \) outside the absolute value indicates a vertical shift upwards by 5 units.

The original function is given by \( y = |x| \). This is the basic absolute value function, which has its vertex at the origin \((0, 0)\).

The transformed function is \( y = |x - 1| + 5 \). Here, the term \( |x - 1| \) indicates a horizontal shift to the right by 1 unit, moving the vertex from \((0, 0)\) to \((1, 0)\). The \( +5 \) indicates a vertical shift upwards by 5 units, moving the vertex to \((1, 5)\).

Thus, the shifts that have occurred are:

• Horizontal shift: \( \text{right } 1 \)
• Vertical shift: \( \text{up } 5 \)

Final Answer