Question

Function g is defined below.

g(x)=f(x+2)-5

Complete the statements about the effects of the transformations on the graph of function f to obtain the graph of function g.

The graph of function f is shifted__ 2 units and__ 5 units.

If the point (4,-3) is on the graph of function f, then the point (_,_) is on the graph of function g.

Answer 1

Answers:

The graph of function f is shifted left 2 units and down 5 units.

If the point (4,-3) is on the graph of function f, then the point (2,-8) is on the graph of function g.

Step-by-step explanation:

1) Adding a positive constant value to the argument of a function shifts its graph as many units to the left as the value of the number. If the number is negative then the shift is to the right.

2) Adding a positive constant value to the function output shifts its graph as many units up as the value of the number. If the number is positive then the shift is to the right.
3) Using that the point (4,-3) will be:

- shifted 2 units to the left ⇒ 4 - 2 = 2, and
- shifted 5 units down ⇒ - 3 - 5 = - 8
⇒ (4,-3) → (2, -8)