Question

Let f(x)=3x and g(x)=3x−3+2 .

Which transformations are needed to transform the graph of f(x) to the graph of g(x) ?

Use the drop-down menus to complete the statements.

Answer 1

Horizontal Translation of 3 units to the right

Vertical Translation of 2 units up

Answer 2

Transformations: Shifted down by 3 units.

Then Shifted up by 2 units.

Explanation:

Let the parent function be f(x) = 3x

Now shift the parent graph down by 3 units

Rule : f(x)→f(x)-b

The graph f(x) shifted down by b units

So, According to rule f(x)→f(x)-3

So, new function becomes: f'(x)=3x-3

Now we are supposed to shift the graph 2 units up

Rule : f(x)→f(x)+b

The graph f(x) shifted up by b units

So, According to rule f'(x)→f'(x)+2

So, the new function is g(x) = 3x-3+2

Thus the graph of f(x) shifted down by 3 units then shifted up by 2 units to obtain the graph g(x).

Transformations: Shifted down by 3 units.

Then Shifted up by 2 units.