How does the graph of the transformed functionf left parenthesis x right parenthesis equals 4 superscript x plus 5 baseline minus 2 compare to the graph of its parent function f left parenthesis x right parenthesis equals 4 superscript x baseline?

Question

(1 point)
Responses

The transformed function is a translation of the parent function right 2 units and up 5 units.
The transformed function is a translation of the parent function right 2 units and up 5 units.

The transformed function is a translation of the parent function left 5 units and down 2 units.
The transformed function is a translation of the parent function left 5 units and down 2 units.

The transformed function is a translation of the parent function left 2 units and up 5 units.
The transformed function is a translation of the parent function left 2 units and up 5 units.

The transformed function is a translation of the parent function right 5 units and down 2 units.
The transformed function is a translation of the parent function right 5 units and down 2 units.

Answer 1

To analyze the transformation of the function \( f(x) = 4^x + 5 - 2 \) compared to the parent function \( f(x) = 4^x \), we can simplify the transformation step-by-step.

1. Identify the transformation:

   • The expression \( f(x) = 4^x + 5 - 2 \) can be simplified to \( f(x) = 4^x + 3 \).
   • This indicates a vertical shift.

2. Vertical Shift:

   • The term \( +3 \) suggests that the graph of \( f(x) = 4^x \) is shifted upward by 3 units.

3. No Horizontal Shift:

   • There are no \( x \) terms added or subtracted from \( 4^x \), which means there is no horizontal translation involved.

Thus, the transformed function \( f(x) = 4^x + 3 \) is a vertical translation of the parent function \( f(x) = 4^x \) up 3 units.

None of the options provided exactly match this conclusion, but based on the common transformations usually encountered, the provided options appear to be incorrect.

If you can clarify the terms \( +5 \) and \( -2 \), it seems there might be no horizontal translation, only a vertical translation of up 3 units.

Please verify the function notation used in your question, as that is crucial for accurate transformations.