Question

brad graphs the function ( y = |x - 2| ). cindy graphs the function ( y = -|x - 2| ). how does cindy’s graph compare to brad’s graph?

• cindy’s graph is one unit to the left of brad’s graph.
• cindy’s graph is a reflection of brad’s graph across the y - axis.
• cindy’s graph is a reflection of brad’s graph across the x - axis.
• cindy’s graph is one unit to the right of brad’s graph.

Explanation:

Step1: Recall transformation rules

The function Brad graphs is \( y = |x - 2| \), and Cindy graphs \( y=-|x - 2| \). For a function \( y = f(x) \), the transformation \( y=-f(x) \) represents a reflection across the \( x \)-axis.

Step2: Analyze each option

• Option 1: A horizontal shift left would be \( y = |x - 2+1|=|x - 1| \), not Cindy's function. Eliminate.
• Option 2: A reflection across \( y \)-axis would be \( y = |-x - 2|=|x + 2| \), not Cindy's function. Eliminate.
• Option 3: Since \( y=-|x - 2| \) is \( -f(x) \) where \( f(x)=|x - 2| \), this is a reflection across \( x \)-axis. Correct.
• Option 4: A horizontal shift right would be \( y = |x - 2 - 1|=|x - 3| \), not Cindy's function. Eliminate.

Answer:

Cindy's graph is a reflection of Brad's graph across the x - axis. (The option corresponding to this statement, e.g., if it's the third option in the list, then: C. Cindy's graph is a reflection of Brad's graph across the x - axis)