Asked by keckagurl forever on Jul 06, 2024
Verified
Identify the transformations of the graph of f(x) =x2f ( x ) = x ^ { 2 }f(x) =x2 that would produce the graph of h(x) =−(x+3) 2+4h ( x ) = - ( x + 3 ) ^ { 2 } + 4h(x) =−(x+3) 2+4 .
A) horizontal shift 3 units left; vertical shift 4 units upward
B) horizontal shift 3 units right; reflection in the x -axis; vertical shift 4 units downward
C) horizontal shift 4 units right; vertical shift 3 units downward
D) horizontal shift 4 units left; reflection in the x -axis; vertical shift 3 units upward
E) horizontal shift 3 units left; reflection in the x -axis; vertical shift 4 units upward
Transformations
A function that moves or changes a shape in some way on the coordinate plane, including translations, rotations, reflections, and dilations.
Graph
A visual representation of data, equations, or functions, typically drawn on a coordinate plane.
- Execute modifications on the curve of \((x^2)\).
Verified Answer
DW
Dustin WilliamsJul 11, 2024
Final Answer :
E
Explanation :
The graph of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 represents a parabola with the vertex at the origin. The negative sign in front of the expression (x+3)2( x + 3 ) ^ { 2 }(x+3)2 indicates that the parabola is reflected in the x-axis. The +3+3+3 inside the parentheses indicates a horizontal shift 3 units to the left. Finally, the +4+4+4 outside the parentheses indicates a vertical shift 4 units upward. Therefore, the transformation sequence is a horizontal shift 3 units left, reflection in the x-axis, and a vertical shift 4 units upward, which corresponds to answer choice E.
Learning Objectives
- Execute modifications on the curve of \((x^2)\).