Answer :
Answer:Rewrite the function: [ Y = 3(-8x - 4) ] Factor out the -8 from the expression inside the parentheses: [ Y = 3[-8(x + \frac{1}{2})] ] Simplify: [ Y = -24(x + \frac{1}{2}) ]
Identify the parent function: The parent function here is ( Y = x ).
Describe the transformations:
Horizontal shift: The term ( (x + \frac{1}{2}) ) indicates a horizontal shift to the left by (\frac{1}{2}) units.
Vertical stretch and reflection: The coefficient -24 indicates a vertical stretch by a factor of 24 and a reflection across the x-axis.
So, compared to the parent function ( Y = x ):
The graph is shifted left by (\frac{1}{2}) units.
It is vertically stretched by a factor of 24.
It is reflected across the x-axis.
Would you like to see a visual representation of these transformations?
Step-by-step explanation:
