Question

question 1 of 10
which of the following is a parent function?

a. $f(x) = e^x$

b. $f(x) = 2 \cdot 3^x$

c. $f(x) = x^4 + 3$

d. $f(x) = 2e^{2x}$

Explanation:

A parent function is the simplest form of a function in a family of functions, without transformations (like vertical/horizontal shifts, stretches/compressions, reflections).

• Option A: \( f(x) = e^x \) is the natural exponential parent function (no coefficients, transformations).
• Option B: \( 2 \cdot 3^x \) has a coefficient (2) and base 3 (not the natural base \( e \) for the exponential parent, and the coefficient is a transformation).
• Option C: \( x^4 + 3 \) has a vertical shift (+3), so it’s a transformed version of \( x^4 \).
• Option D: \( 2e^{2x} \) has coefficients (2) and a horizontal compression (exponent \( 2x \)), so it’s transformed.

Only A is in the simplest parent function form.

Answer:

A. \( f(x) = e^x \)