The expression of G(x) when shifted to left 3 units is 2( x+3) ^2 -1.
A function can then be defined as a set of ordered pairs. Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
For the given situation,
The original function F(x) = 2x^2 - 1.
The general equation of a parabola is y = a(x-h)^2 + k.
The function is shifted to the left 3 units to make the function G(x)
so we need to add -3 to x,
⇒ [tex]G(x) = 2(x-(-3))^{2} -1[/tex]
⇒ [tex]G(x) = 2(x+3)^{2} -1[/tex]
Hence we can conclude that the expression of G(x) when shifted to left 3 units is 2( x+3) ^2 -1.
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