Respuesta :
Answer:
B, E and F.
Step-by-step explanation:
The transformation f(x) ------> f(x + a) moves f(x) a units to the left.
So when there is an increase in the number added to x in the parentheses the graph moves to the left.
So B is one because of the (x - 1)2 ---> (x + 1)2
The others are E and F.
The functions which has a graph in which the vertex and axis of symmetry are left of the vertex and axis of symmetry of the provided graph of f(x) are,
[tex]g(x) = -(x + 1)^2 - 2\\g(x) = -(x + 2)^2 + 2\\g(x) = 2(x + 1)^2 + 2[/tex]
What is transformation of a function?
Transformation of a function is shifting the function from its original place in the graph.
Types of transformation-
- Horizontal shift-Let the parent function is [tex]f(x)[/tex]. Thus, by replacing parent function with [tex]f(x-b)[/tex] Shifts the graph b units right, and by replacing parent function with [tex]f(x+b)[/tex] shifts the graph b units left.
- Vertical shift-Let the parent function is [tex]f(x)[/tex]. Thus, by replacing parent function with [tex]f(x)+c[/tex] shifts the graph c units down and by replacing parent function with [tex]f(x)-c[/tex] Shifts the graph b units up.
The function of the graph is,
[tex]f(x) = (x -1)^2 + 1[/tex]
The function to be left of the vertex of the above function, b units must be added in the parent function such that,
[tex]f(x+b)[/tex].
The option B, E and F looks like this function.
Thus, the functions which has a graph in which the vertex and axis of symmetry are left of the vertex and axis of symmetry of the provided graph of f(x) are,
[tex]g(x) = -(x + 1)^2 - 2\\g(x) = -(x + 2)^2 + 2\\g(x) = 2(x + 1)^2 + 2[/tex]
Learn more about the transformation of a function here;
https://brainly.com/question/10904859
