vapicc42
Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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].
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.