HELP PLEASE!!! 25 Points & Brainliest!1) The function f(x)=3x+4 is a linear function. Let g(x) represent f(x) after a horizontal translation 2 units to the left. What is the equation for the function g(x)?Enter your answer in the box.g(x) = ___2) Consider the function f(x)=−2/3x+2.What is f(1/2)?Enter your answer, as a simplified fraction, in the box.f(1/2)=___3) Which answer is an equation in point-slope form for the given point and slope?point: (1,−9) ; slope: 2a) y+9=2(x−1)b) y+9=2(x+1)c) y−9=2(x+1)d) y−9=2(x−1)

Accepted Solution

Answer:(1) [tex]f(x)=3x+4[/tex]Ad g(x) represent f(x) after horizontal translation 2 units to the left.[tex]g(x)=3(x+2)+4[/tex][tex]g(x)=3x+6+4[/tex][tex]g(x)=3x+10[/tex] is the required translation.(2) [tex]f(x)=\frac{-2x}{3}+2[/tex][tex]f(\frac{1}{2})=\frac{-2}{3}\cdot(\frac{1}{2})+2[/tex][tex]f(\frac{1}{2})=\frac{5}{3}[/tex](3) We have been given a point (1,-9); slope 2We will use the equation:[tex]y-y_1=m(x-x_1)[/tex]m is the give slope.[tex]y-(-9)=2(x-1)[/tex][tex]y+9=2(x-1)[/tex]Therefore, Option (a) is correct.