Respuesta :

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f(x)=2x^2 -1 
Translation is a function transformation that transform the function in a way of translating. By translating the function its graph is moved up an down. Moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1

Answer:

[tex]g(x) = 2(x+2)^2 -1[/tex]

Step-by-step explanation:

In general if a function f translated a units left  i,e

y =f(x) translated by a units left we have;

y =f(x+a)

Given the function:

[tex]f(x) = 2x^2-1[/tex]

We have to find the function g(x):

g(x) is f(x) translated left 2 units

By definition we have;

⇒[tex]g(x) = f(x+2)[/tex]

⇒[tex]g(x) = 2(x+2)^2 -1[/tex]

Therefore, the equation of g(x) is,

[tex]g(x) = 2(x+2)^2 -1[/tex]