Question

The function f(x)=−4x+3 is a linear function. Let g(x) represent f(x) after a horizontal translation 2 units to the left. What is the equation for g(x) ? Enter the answer in the box. g(x) = ( please help me i am in tears )

Answer 1

Let me help you with that. Simply put, it is 4x+1.
It keeps the same slope, but just starts over to the left 2 from the original equation.

Answer 2

Following are the calculation to the g(x) function:

Given:

f(x)=-4x+3

g(x)=f(x) after a horizontal translation 2 units

To find:

g(x)=?

Solution:

A horizontal translation, in short, implies f("x + some number"), its value is now 2, and this is to the left, so f(x + 2)

$\to \bold{\left \{ {{f(x)=-4x+3} \atop {g(x)=f(x+2)}} \right} \\\\\\\to \bold{f(x+2)}=-4(x+2)+3}$

                 $\bold{= -4x-8+3}\\\\ \bold{=-4x-5}$

$\therefore \\\\\to \bold{g(x)= -4x-5} = \bold{-(4x+5)}$

Therefore, the final answer is "$\bold{-(4x+5)}$"

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