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Which statement describes the graph of g(x) with respect to the graph f(x)?

a. let f(x)=(x+3)^2+2
let g(x)=(x+3)^2-3
* it is translated right 5 units
* stretched horizontally by a
factor of -3
* compressed vertically by a
factor of -3
* it is translated down 5 units


b. let f(x)=x^2 +5
let g(x)=(x+1)^2+5
* it is translated right 1 unit
* it is translated left 1 unit
*it is translated up 1 unit
* compressed vertically by a
factor of 5

c. Let f(x)=(x+6)^2
let g(x)=2(x+6)^2
* it is compressed horizontally by a factor of 2
* it is translated up 2 units
* it is translated right 2 units
* it is stretched vertically by a factor of 2

show work and answer please

Respuesta :

Answer:

a. Translated down  5 units.

b.  Translated 1 to the left.

c.  Stretched vertically  by a factor 2.

Step-by-step explanation:

a. It is translated down by 2 - (-3) = 5 units.

b. The x in f(x) is replaced by (x + 1) to gives g(x).

It is translated left by 1 unit.

c.  The 2 stretches it vertically by a factor of 2.

Using translation concepts, it is found that the correct options are given by:

a) it is translated down 5 units.

b) it is translated left 1 unit.

c) it is stretched vertically by a factor of 2.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem:

  • In item a, 5 was subtracted from the function, hence it was shifted down 5 units.
  • In item b, we have that x -> x + 1, hence it was shifted left 1 unit.
  • In item c, the function was multiplied by 2, hence it was vertically stretched 2 units.

More can be learned about translation concepts at https://brainly.com/question/4521517

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