Mathematics

Question

Let f(x)=2x2−1.
The quadratic function g(x) is f(x) translated left 2 units.
Enter the equation of g(x) in the box.

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2 Answer

  • 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]

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