I'm in desperate need of help on how to do these 4 problems.

Write the function g(x) with the indicated transformations.

1. f(x)=x; translated right 3 units

2. f(x)=x^2; vertical stretch by 5, translated down 3 units and reflected across the x-axis

3 f(x)=|x|; vertical shrink by 1/4, and right 1 unit and up 2 units

4. f(x)=-(x-4)^2; vertical stretch by a factor of 3, translated up 2 and right 8

#1 g(x) = f(x-3) = x-3

#2 g(x):
stretch y by 5: 5f(x)
down 3: 5f(x)-3
x reflect: -(5f(x)-3) = 3 - 5f(x)
g(x) = 3 - 5x^2

#3 g(x):
shrink y by 4: (1/4)f(x)
right 1: (1/4)f(x-1)
up 2: (1/4)f(x-1)+2
g(x) = (1/4)|x-1|+2

#4 g(x):
y stretch 3: 3f(x)
up 2: 3f(x)+2
right 8: 3f(x-8)+2
g(x) = 3[-((x-8)-4)^2)]+2 = 2-3(x-12)^2

Sure! I can help you with these problems. Let's go through each problem step by step and explain how to get the answer.

1. f(x) = x; translated right 3 units:
To translate the function f(x) = x right 3 units, you need to subtract 3 from the x-coordinate of every point on the graph. This means that the value of x gets replaced with (x - 3). So the function g(x) with this transformation would be g(x) = (x - 3).

2. f(x) = x^2; vertical stretch by 5, translated down 3 units, and reflected across the x-axis:
To vertically stretch a function, you multiply the y-coordinate of every point on the graph by the vertical stretch factor. In this case, the vertical stretch factor is 5, so you multiply every y-coordinate by 5. To translate the function down 3 units, you subtract 3 from the y-coordinate of every point. Finally, to reflect the function across the x-axis, you negate the y-coordinates. So putting it all together, the function g(x) with these transformations would be g(x) = -5(x^2) - 3.

3. f(x) = |x|; vertical shrink by 1/4, right 1 unit, and up 2 units:
To vertically shrink a function, you multiply the y-coordinate of every point on the graph by the vertical shrink factor. In this case, the vertical shrink factor is 1/4, so you multiply every y-coordinate by 1/4. To translate the function right 1 unit, you add 1 to the x-coordinate of every point. And to translate the function up 2 units, you add 2 to the y-coordinate of every point. So the function g(x) with these transformations would be g(x) = (1/4)|x - 1| + 2.

4. f(x) = -(x - 4)^2; vertical stretch by a factor of 3, translated up 2, and right 8:
To vertically stretch a function, you multiply the y-coordinate of every point on the graph by the vertical stretch factor. In this case, the vertical stretch factor is 3, so you multiply every y-coordinate by 3. To translate the function up 2 units, you add 2 to the y-coordinate of every point. Finally, to translate the function right 8 units, you subtract 8 from the x-coordinate of every point. So the function g(x) with these transformations would be g(x) = 3(-(x - 8 - 4)^2) + 2.

Please note that in some steps, I simplified the expressions by performing necessary calculations. Make sure to carefully follow the sequence of transformations and simplify the expression as needed.