Question

enter the equation (f(x) = 2^x) and (g(x) = 2^x + 1) in the desmos graphing calculator. how does g(x) differ from the graph of f(x)?

• the graph translates to the left 1 unit
• the graph translates up 1 unit.
• the graph translates down 1 unit.
• the graph translates to the right 1 unit

Explanation:

Compare the two functions

Using the Function Transformations knowledge point

$$ g(x) = f(x) + 1 $$

Determine the transformation type

Using the Function Transformations knowledge point

$$ y = f(x) + k \implies \text{Vertical translation by } k \text{ units} $$

$$ k = 1 > 0 \implies \text{Shift up by 1 unit} $$

Answer:

• The graph translates to the left 1 unit
• The graph translates up 1 unit. (Correct answer)
• The graph translates down 1 unit.
• The graph translates to the right 1 unit