Translations of Exponential Functions

What is the initial function set up in the Desmos graphing calculator?

• y = 2x

• y = x^2

• y = x + 2

• y = 2^x

By how many units is the graph of y = 2^x shifted up when 3 is added outside the exponent?

• 3 units

• 5 units

• 1 unit

• 2 units

What is the effect of subtracting 5 from y = 2^x on the graph's position?

• Shifts right by 5 units

• No shift

• Shifts down by 5 units

• Shifts up by 5 units

How does adding 2 inside the exponent of y = 2^x affect the graph?

• Moves it right by 2 units

• Moves it left by 2 units

• Moves it down by 2 units

• Moves it up by 2 units

What general rule applies to the translation of exponential functions when modifying the exponent?

• Minus inside exponent shifts left

• No shift occurs

• Plus inside exponent shifts left

• Plus inside exponent shifts right

If the function y = 1/2^x is changed to y = 1/2^(x + 8), how is the graph translated?

• 8 units up

• 8 units down

• 8 units left

• 8 units right

What does a subtraction of 2 at the end of the function y = 9^x indicate about the graph's translation?

• 2 units up

• 2 units down

• 2 units right

• 2 units left

In the function y = 4^(x - 3) + 5, what are the transformations applied to the graph?

• 3 units left and 5 units down

• 3 units right and 5 units up

• 3 units left and 5 units up

• 3 units right and 5 units down

How does the graph of y = 4^(x + 6) - 1 translate compared to its parent function?

• 6 units left and 1 unit down

• 6 units right and 1 unit up

• 6 units left and 1 unit up

• 6 units right and 1 unit down

What transformation is applied to the function y = 8^(x - 2) - 1?

• 2 units left and 1 unit up

• 2 units right and 1 unit down

• 2 units left and 1 unit down

• 2 units right and 1 unit up