Question

given ( a(x) = 8^x ), if ( a(x) ) is vertically stretched by a factor of 4 and reflected across the ( y )-axis, what is the new expression of ( a(x) )? (1 point)
( circ ) ( a(x) = 8^x - 4 )
( circ ) ( a(x) = 8^{-4x} )
( circ ) ( a(x) = -4 cdot 8^{-x} )
( circ ) ( a(x) = 4 cdot 8^{-x} )

Explanation:

Step1: Recall Vertical Stretch Transformation

A vertical stretch by a factor of \( k \) on a function \( f(x) \) transforms it to \( k \cdot f(x) \). For \( a(x)=8^{x} \), a vertical stretch by factor 4 gives \( 4 \cdot 8^{x} \).

Step2: Recall Reflection Across y - axis Transformation

A reflection across the \( y \)-axis on a function \( f(x) \) transforms it to \( f(-x) \). Applying this to \( 4 \cdot 8^{x} \), we replace \( x \) with \( -x \), so we get \( 4 \cdot 8^{-x} \).

Answer:

\( a(x) = 4\cdot 8^{-x} \) (corresponding to the option \( a(x)=4\cdot 8^{-x} \))