contestada

Fas
5. If f(x) = x3 is changed to g(x) = 2f(x – 3), how is the
graph transformed?
=
A. The graph is vertically stretched by a factor of 2 and
translated 3 units right.
B. The graph is vertically compressed by a factor of 2
and translated 3 units left.
C. The graph is vertically stretched by a factor of 2 and
translated 3 units left.
D. The graph is vertically compressed by a factor of 2
and translated 3 units right.

Respuesta :

The graph is vertically stretched by a factor of 2 and translated 3 units right when it is transformed. Option A is correct.

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 f(x). Thus by replacing parent function with f(x-b) shifts the graph b units right and by replacing parent function with f(x+b) shifts the graph b units left.
  • Vertical shift- Let the parent function is f(x). Thus by replacing parent function with f(x)-c shifts the graph c units down and by replacing parent function with f(x)+c shifts the graph c units up.

The given function is,

[tex]f(x) = x^3[/tex]

This function is changed to the function,

[tex]g(x) = 2f(x -3),[/tex]

Here the 3 units is substrate in the function. Thus, it is shiftet 3 units right. The number 2 is multiplied in the function which vertically stretched the graph by a factor of 2.

Thus, the graph is vertically stretched by a factor of 2 and translated 3 units right when it is transformed. Option A is correct.

Learn more about the transformation of a function here;

https://brainly.com/question/10904859

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