LileyhaperSibylara
contestada

Functions f(x) and g(x) are shown below. f(x) = x2. . g(x) = x2 - 8x + 16. In which direction and by how many units should f(x) be shifted to obtain g(x)? A. Left by 4 units
B. Right by 4 units
C. Left by 8 units
D. Right by 8 units

Respuesta :

carlosego
The original function is given by:
 [tex]f (x) = x ^ 2 [/tex]
 We apply the following transformation:
 Horizontal displacements:
 Suppose k> 0
 To move the graph k units to the right, we must graph f (x-k)
 Applying the transformation for k = 4 we have:
 [tex]g (x) = f (x-4) g (x) = (x-4) ^ 2 g (x) = x ^ 2 - 8x + 16[/tex]
 Answer:
 B. Right by 4 units

Answer:

Option B is correct.

Right by 4 units

Step-by-step explanation:

Given the function : [tex]f(x) = x^2[/tex] and [tex]g(x)=x^2-8x+16[/tex]

Horizontal shift: Given a function f , a new function g(x) = f(x-h) , where h is constant is a horizontal shift of the function f.

* If h is positive, the graph will shift right.

* if h is negative, then the graph will shift left.

[tex]g(x)=x^2-8x+16[/tex]

[tex]x^2 -4x-4x +16[/tex]

[tex]x(x-4)-4(x-4)[/tex]

Take (x-4) common;

[tex](x-4)(x-4)[/tex] or

[tex](x-4)^2[/tex]                    [ Using [tex]a^m \cdot a^n = a^{m+n}[/tex] ]

Then, the function becomes;

g(x) = [tex](x-4)^2[/tex]

A function g(x)=[tex](x-4)^2[/tex] , this function comes from the parent function [tex]f(x) = x^2[/tex]  with constant 4 subtract to it, this gives the horizontal shift right 4 units. so, take the parent function and shift 4 units right.

Therefore, a function f(x) be shifted right by 4 unit  to obtain g(x)


Otras preguntas