The parent function is 2ˣ
What are Parent functions?
The simplest function in a family of functions that maintains the definition (or shape) of the entire family is called a parent function.
These fundamental functions include the square root function, basic polynomials, absolute values, and rational and exponential functions.
Given,
option(A) f(x) = 3ˣ ₋ x/3, here the parent function is y = 3ˣ but in this case it is translated so the translated function cannot be a parent function.
option(B) f(x) = ₋3x³₊1, here the parent function can be y = x³, but it is reflecting across the x-axis, vertically stretching a factor of 3 and shifting 1 unit upwards.
option(C) f(x) = 1/2 3ˣ, here parent function can be y = 3ˣ but it vertically shrinks a factor of 1/2.
option(D) f(x) = 2ˣ, here parent function is y = 2ˣ as it is not a translated function it is in its base form.
Hence we get the parent function as f(x) = 2ˣ
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