Which of the following is a parent function?A.𝑓(𝑥)=−2𝑥+1f(x)=−2 x+1 B.𝑓(𝑥)=𝑒3𝑥−2f(x)=e 3x −2C.𝑓(𝑥)=4𝑥f(x)=4 x D.𝑓(𝑥)=4𝑥2f(x)=4x 2 SUBMITarrow_backPREVIOUS

Understanding Parent Functions

A parent function is the simplest form of a function that still maintains the general characteristics of that function type. For polynomial functions, the simplest forms are often just the variable raised to a power multiplied by a constant.

Analyzing the Options

1. A. $f(x) = -2x + 1$
   This is a linear function, but the parent function for linear equations is typically $f(x) = x$.

2. B. $f(x) = e^{3x} - 2$
   This is an exponential function, but the simplest form is $f(x) = e^x$.

3. C. $f(x) = 4x$
   This is a linear function as well, with the parent function being $f(x) = x$.

4. D. $f(x) = 4x^2$
   This is a quadratic function. The parent function for quadratic functions is $f(x) = x^2$.

Final Verification and Conclusion

Among the choices, D $4x^2$ is the only option that can be considered a transformation of the parent function $f(x) = x^2$. The multiplier (4) does not change the fact that it is still fundamentally a parabolic function.

Final Answer

D. $f(x) = 4x^2$ is a parent function.