1. Find g (x), where g (x) is the translation 7 units up of f (x) = x.

2. Find g (x), where g (x) is the translation 5 units left of f (x) = x2.

3. Find g (x), where g (x) is the translation 3 units right and 4 units up of f (x) = x2.

4. Find g (x), where g (x) is the translation 1 unit left and 5 units down of f (x) = |x|.

See explanation

Step-by-step explanation:

Solution:-

- Here we will take a look at the effect of translation on the original graph.

- Where, f (x) is the original given function which undergoes translation (up, down, right or left) and result in g (x).

- The general form of all possible translations are given:

Vertical Translation

g (x) = f (x) + a

Where, a > 0 ... number of units the f (x) moves up

a < 0 ... number of units the f (x) moves down

Horizontal Translation

g (x) = f (x + b)

Where, b > 0 ... number of units the f (x) moves left

b < 0 ... number of units the f (x) moves right

part a)

f (x) = x

Where, f (x) undergoes a vertical translation of 7 units up.

So using the first case with value of a = + 7

g (x) = f (x) + 7

g (x) = x + 7

part b)

f (x) = x^2

Where, f (x) undergoes a horizontal translation of 5 units left.

So using the second case with value of b = + 5

g (x) = f (x + 5)

g (x) = (x + 5) ^2

part c)

f (x) = x^2

Where, f (x) undergoes two translations; horizontal translation of 3 units right and a vertical translation of 4 units up.

So using the first and second case with value of a = + 4, b = - 3

g (x) = f (x - 3) + 4

g (x) = (x - 3) ^2 + 4

part d)

f (x) = absolute (x)

Where, f (x) undergoes two translations; horizontal translation of 1 unit left and a vertical translation of 5 units down.

So using the first and second case with value of a = - 5, b = + 1

g (x) = f (x + 1) - 5

g (x) = absolute [ (x + 1) ] - 5