Respuesta :
Answer:
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
