Keywords:
Transformation of functions, vertical translations, horizontal translations
For this case we have to define function transformation:
Vertical translations:
Let [tex]a> 0[/tex], to graph [tex]y = f (x) + a[/tex], move the graph of [tex]f (x)[/tex] "a" upwards.
Horizontal translations:
Let [tex]b> 0[/tex], to graph [tex]y = f (x-b)[/tex], we must move the graph of [tex]f (x)[/tex]"b" units to the right.
If we have as initial function [tex]h (x) = | x |[/tex]
To obtain [tex]g (x) = | x-3 |[/tex] we move the graph of[tex]h (x) = | x |[/tex] three units on the right.
To obtain [tex]f (x) = | x-3 | +6[/tex] we move the graph of [tex]g (x) = | x-3 |[/tex]six units up.
Thus, the vertex of[tex]f (x) = | x - 3 | + 6[/tex] is located at: [tex](x, y) = (3,6)[/tex]
Answer:
The vertex of the graph of [tex]f (x) = | x - 3 | + 6[/tex] is located at: [tex](x, y) = (3,6)[/tex]
If we subtract 3 from the variable then the graph shift towards the right by 3 units. And if we add 6 in the function then the graph shifts upward by 6 units.
The vertex of the function is at (3, 6)
The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
Given
The function is f(x) = |x – 3| + 6.
To find
The vertex of the graph.
Let, the function is f(x) = |x|
We know that if we subtract 3 from the variable then the graph shift towards the right by 3 units. Then f(x) will be.
f(x) = |x – 3|
And if we add 6 in the function then the graph shifts upward by 6 units. Then f(x) will be.
f(x) = |x – 3| + 6.
The graph is shown.
By the graph, the vertex is at (3, 6)
More about the function link is given below.
https://brainly.com/question/5245372
