contestada

Describe how the graph of each function can be obtained from the graph of y = f(x). Make sure you use full sentences to explain the transformation of the new function.
a) y=3f(x)–2
(b) y=f(x-1)–4
(c) y=f(1⁄2x)+5

Respuesta :

Using translation concepts, the changes are described as follows:

a) The function is vertically stretched by a factor of 3, and shifted down 2 units.

b) The function is shifted 1 unit right and 4 units down.

c) The function is horizontally compressed by a factor of 2 and shifted up  5 units.

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.

Item a:

The changes are as follows:

  • y -> 3y, hence the function is vertically stretched by a factor of 3.
  • y -> y - 2, hence the function is shifted down 2 units.

Item b:

The changes are as follows:

  • x -> x - 1, hence the function is shifted right 1 unit.
  • y -> y - 4, hence the function is shifted down 4 units.

Item c:

The changes are as follows:

  • x -> 0.5x, hence the function is horizontally compressed by a factor of 2.
  • y -> y + 5, hence the function is shifted up 4 units.

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

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