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Which description explains how the graph of f(x)=√x could be transformed to form the graph of g(x) = √x-6

horizontal shift of 6 units left
horizontal shift of 6 units right
vertical stretch by a factor of 6
vertical shift of 6 units up

Which equation represents the transformation of f(x)=|x| when effected by a vertical stretch of 3, a horizontal shift to the right 4 units, and a vertical shift up 2 units?

g(x)= 1/3 |x−4| + 2

g(x)= 1/3 |x+4| − 2

g(x)= 3 |x−4| + 2

g(x)= 3 |x+4| + 2

Respuesta :

wishmorethewitch

Answer:

b

c

Step-by-step explanation:

First question: x - 6 means there is a shift to the right.

Second Question: substitute the given values into the original equation for appropriate transformations.

Answer: 3 |x-4| + 2, because vertical stretch multiplies x, horizontal shifts are subtracted or added to x, and vertical shifts are added or subtracted to the entire function.

The movement of the curve in the graph is shifting of the curve in vertical or the horizontal direction.For the first function the graph horizontal shift of 6 units right and for the second function when it is  vertical stretch of 3, a horizontal shift to the right 4 units, and a vertical shift up 2 units the transformation function is,

[tex]g(x)=3|x-4|+2[/tex]

Given-

The equation of the graph given in the problem is,

[tex]f(x)=\sqrt{x} [/tex]

Translation of the graph

The movement of the curve in the graph is shifting of the curve in vertical or the horizontal direction.

  • a) The equation of the graph when it is transferred is given as,

          [tex]g(x)=\sqrt{x-6} [/tex]

There is no change with the constant value. Thus the graph will not move in vertical direction. The change in variable of a unit result in the graph shift in horizontal direction.

As it shift -6 thus graph horizontal shift of 6 units right.

  • b) The given function is,

[tex]f(x)=|x|[/tex]

Vertical stretch of 3 means multiply the function with unit 3.

[tex]g(x)=3|x|[/tex]

Horizontal shift to the right 4 units means the difference of 4 units in the variable,

[tex]g(x)=3|x-4|[/tex]

Vertical shifts up with 2 units means the addition of the constant 2.

[tex]g(x)=3|x-4|+2[/tex]

Hence, for the first function the graph horizontal shift of 6 units right and for the second function when it is  vertical stretch of 3, a horizontal shift to the right 4 units, and a vertical shift up 2 units the transformation function is,

[tex]g(x)=3|x-4|+2[/tex]

Learn more about the Translation of the graph here;

https://brainly.com/question/1870192

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