A function, named \( g \), has an input of \( c \) and a range of all real numbers. Which option best represents the described function? \( g(c)=4 c^{2}-2 c+1 \) \( g(c)=\frac{4}{5} c+\frac{2}{5} \) \( c(g)=\frac{4}{5} g+\frac{2}{5} \) \( c(g)=4 g^{2}-2 g+1 \)

To determine the correct option, consider two key points from the description: 1. The function is named g and its input is c. 2. The function's range is all real numbers. Let's evaluate each choice: • g(c) = 4c² - 2c + 1 This is a quadratic (parabolic) function. A quadratic function with a nonzero leading coefficient typically has a restricted range (either all values greater than or equal to a minimum or less than or equal to a maximum). Thus, its range is not all real numbers. • g(c) = (4/5)c + (2/5) This is a linear function. Since it has a nonzero slope (4/5), it is a one-to-one function mapping every real number c to a unique real number. Its range is all real numbers. Also, the function properly shows g as a function of c. • c(g) = (4/5)g + (2/5) Here, the function is written as c in terms of g, which does not match the requirement that the function be g with input c. • c(g) = 4g² - 2g + 1 Similarly, this is a quadratic function defined in terms of g and does not meet the criteria of having g as the function name with input c. Thus, the option that best represents the described function is: g(c) = (4/5)c + (2/5)