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Let [tex][tex]$f(x)=4x^2+6$[/tex][/tex].

The function [tex][tex]$g(x)$[/tex][/tex] is [tex][tex]$f(x)$[/tex][/tex] translated 4 units down.

What is the equation for [tex][tex]$g(x)$[/tex][/tex] in simplest form?

[tex]g(x) = \square[/tex]

Sagot :

GinnyAnswer
Sure, let’s work through this step-by-step.

We start with the function [tex]\( f(x) = 4x^2 + 6 \)[/tex].

We are asked to translate this function 4 units down. Translating a function down by a specific number involves subtracting that number from the function.

To translate [tex]\( f(x) \)[/tex] downward by 4 units, we subtract 4 from [tex]\( f(x) \)[/tex]:

[tex]\[ g(x) = f(x) - 4 \][/tex]

Now, we plug in the expression for [tex]\( f(x) \)[/tex]:

[tex]\[ g(x) = (4x^2 + 6) - 4 \][/tex]

Simplify the expression by combining like terms:

[tex]\[ g(x) = 4x^2 + 6 - 4 \][/tex]
[tex]\[ g(x) = 4x^2 + 2 \][/tex]

So, the equation for [tex]\( g(x) \)[/tex] in its simplest form is:

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

Thus, [tex]\( g(x) = \boxed{4x^2 + 2} \)[/tex].
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