What is the function g(x) created from f(x) = x² by moving the graph left 4 units, vertically stretching it by a factor of 5, and shifting the graph down 8 units?
A g(x) = 4(x + 5)² + 8
B g(x) = 5(x – 4)² + 8
C g(x) = 8(x + 4)² + 5
D g(x) = 5(x + 4)² – 8
What is the function g(x) created from f(x) = x² by moving the graph left 4 units, vertically stretching it by a factor of 5, and shifting the graph down 8 units?
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To find the function ( g(x) ) from ( f(x) = x^2 ) given the transformations:
1. Move the graph left 4 units: This transforms ( f(x) ) to ( f(x + 4) ), which gives ( (x + 4)^2 ).
2. Vertically stretch by a factor of 5: This means we multiply the quadratic by 5, resulting in ( 5(x + 4)^2 ).
3. Shift down 8 units: This subtracts 8 from the whole function, giving us ( 5(x + 4)^2 – 8 ).
So, the final function is ( g(x) = 5(x + 4)^2 – 8 ).
The correct answer is D: ( g(x) = 5(x + 4)^2 – 8 ).