here are graphs of functions f and g. which sequences of transformations take the graph of f to the graph of…

here are graphs of functions f and g. which sequences of transformations take the graph of f to the graph of g? select all that apply. show your work here reflection over the y - axis, then translation up by 2 reflection over the x - axis, then translation up by 2 translation up by 2, then reflection over the y - axis translation up by 2, then reflection over the x - axis translation up by 2, then translation left by 5

here are graphs of functions f and g. which sequences of transformations take the graph of f to the graph of g? select all that apply. show your work here reflection over the y - axis, then translation up by 2 reflection over the x - axis, then translation up by 2 translation up by 2, then reflection over the y - axis translation up by 2, then reflection over the x - axis translation up by 2, then translation left by 5

Answer

Explanation:

Step1: Analyze reflection over y - axis

Reflecting a function (y = f(x)) over the (y) - axis gives (y = f(-x)). Translating (y = f(-x)) up by (2) gives (y=f(-x)+2).

Step2: Analyze translation up then reflection over y - axis

Translating (y = f(x)) up by (2) gives (y = f(x)+2). Reflecting (y = f(x)+2) over the (y) - axis gives (y=f(-x)+2).

Step3: Analyze translation up then left

Let the vertex of (f) be ((x_f,y_f)) and of (g) be ((x_g,y_g)). If we assume a general transformation, for a parabola (since the graph looks like a parabola), if we translate (f) up by (2) and then left by (5). Let (f(x)=a(x - h)^2 + k), then (g(x)=a(x-(h - 5))^2+(k + 2))

Answer:

Reflection over the (y - axis), then translation up by (2); Translation up by (2), then reflection over the (y - axis); Translation up by (2), then translation left by (5)