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

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you