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: 2 a) y+9=2(x−1) b) y+9=2(x+1) c) y−9=2(x+1) d) y−9=2(x−1)

(1)

Ad g(x) represent f(x) after horizontal translation 2 units to the left.

is the required translation.

(2)

(3) We have been given a point (1,-9); slope 2

We will use the equation:

m is the give slope.

Therefore, Option (a) is correct.

 The answers are:

(1)

(2)

(3) (a)

Step-by-step explanation:  The calculations are as follows:

(1) The given function is

We are to find the equation for the function g(x) is it represents f(x) after a horizontal translation of 2 units to the left.

When the function f(x) is translated 2 units to the left, the vertex of the function will shift from (0, 4) to (-2, 4).

So, the equation of g(x) will be

Thus, the equation for g(x) is

(2)  The given function is

We are to find the value of

We have, after putting in the definition of f(x) that

Thus,

(3) We are to find the equation of a line in point-slope form for the following point and slope:

point: (1,−9) ; slope: 2.

We know that the equation of a line in point-slope form passing through the point (a, b) and slope m is given by

Therefore, the equation for the given line will be

Thus, the required equation of the line in point-slope form is

Option (a) is CORRECT.

Hence, all the questions are answered.

1) Figure ABCD has been moved 7 units to the left and 6 units to the right.

Step-by-step explanation:

The easiest way to solve a problem where a simple translation was made, is to move 1 point at a time. Moving one point at a time for the sequence that you believe is correct makes the big problem into small chunks. Once you finish the first one, you can go ahead and move the others. In the end the points of ABCD should align properly with A'B'C'D'.