Which steps will translate f(x) = 3x to g(x) = 3x + 1 + 4?
shift f(x) = 3x one unit up and four units to the right.
shift f(x) = 3x one unit up and four units to the left.
shift f(x) = 3x one unit to the right and four units up.
shift f(x) = 3x one unit to the left and four units up.

For this case we have that the main function is given by:

We apply the following transformation:

Horizontal translations:

Suppose that h> 0

To graph y = f (x + h), move the graph of h units to the left.

For h = 1 we have:

Vertical translations:

Suppose that k> 0:

To graph y = f (x) + k, move the graph of k units upwards

For k = 4 we have:

Shift f(x) = 3x one unit to the left and four units up.

answer: 40.95

step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .