Question

on each coordinate plane, the parent function f(x) = |x| is represented by a dashed line and a translation is represented by a solid line. which graph represents the translation g(x) = |x| - 4 as a solid line?

Explanation:

Step1: Recall Vertical Translation Rule

For a function \( y = f(x)+k \), if \( k>0 \), the graph shifts up \( k \) units; if \( k<0 \), it shifts down \( |k| \) units. Here, \( g(x)=|x| - 4 \), so \( k=-4 \), meaning the parent function \( f(x)=|x| \) (vertex at \( (0,0) \)) shifts down 4 units.

Step2: Analyze Vertex Position

The vertex of \( f(x)=|x| \) is \( (0,0) \). After shifting down 4 units, the vertex of \( g(x) \) should be \( (0, - 4) \). Now check the graphs:

• First graph: Solid line vertex at \( (0, - 4) \), dashed line (parent) at \( (0,0) \). This matches the vertical shift down 4.
• Second graph: Solid line vertex at \( (0,4) \) (shift up 4), incorrect.
• Third graph: Solid line vertex at \( (4,0) \) (horizontal shift), incorrect.
• Fourth graph: Solid line vertex at \( (-4,0) \) (horizontal shift), incorrect.

Answer:

The first graph (with the solid line vertex at (0, -4))