Question

How is the graph of y = 2(3)^x+1 - 4 translated from the graph of y = 2(3)^x?

please explain all algebraic steps
4 units right and 1 unit up

1 unit right and 4 units up

4 units left and 1 unit down

1 unit left and 4 units down

Answer 1

Option D

Explanation:

In this question parent graph is y = 2(3)ˣ

and the translated graph is y = 2(3)ˣ⁺¹ -4

Translations done.

(1) Parent graph y = 2(3)ˣ is shifted one unit left on x-axis to form y' = 2(3)ˣ⁺¹

(2) Then y' is shifted 4 units down on y-axis giving the translated form y = 2(3)ˣ⁺¹ -4

Option D is the answer.

Answer 2

Translate the graph of y = 2(3)^x one unit to the left and four units down.

Explanation:

It's essential to use parentheses around the exponent in this problem, to avoid ambiguity: y = 2(3)^{x+1} - 4.

The original exponent was x. This new exponent {x+1} represents a translation of the graph of y = 2(3)^x 1 unit to the left.

That -4 translates this resulting graph 4 units down.