Which of these is a parent function? And can you tell me how you know?

Hey there!

A parent function is the most basic function in any group of functions. For example, f(x) = x^2 is the parent function for quadratic functions, and y = x is the parent function for linear functions. When there's nothing added, subtracted, multiplied, or divided to the function.

For A, we see that we're multiplying 2 times 3^x, and since this is not any alternation of any parent function or any parent function in particular, we can rule it out.

For B, we see that 3 is being added to x^2, so it cannot be a parent function.

For C, we see that 2 multiplied to e, therefore it cannot be the mot basic function.

Finally, for D, we see a function that looks similar to the quadratic parent function and is very simple itself. Any alterations to this is any other quadratic function

Your answer is D.

Hope this helps!