Find the domain and range of the function f(x) = 3x^2 - 5.also find f(-3) and the numbers which are associated with the number 43 in the range.

Domain:

This function is a polynomial, i.e. a sum of powers of a variables, each with its coefficient. Polynomials are defined for every possible value of the variable, so the domain is the whole real number set:

Range:

A polynomial of degree 2 represents a parabola. Since the leading coefficients, i.e. the coefficient of the term with highest degree, is positive (in this case, it's 3), the parabola is concave up. It means that it has a minimum, and it's unbounded from above. So, the range is something like . To find the minimum, let's start with the "standard" parabola , and transform it to the one of this exercise. has minimum 0, and thus its range is . When you multiply it times three, its shape narrows, but the range wont change: . Finally, when you subtract 5, you shift everythin down 5 units. This transformation affects the range, since you have

Image of -3:

To compute , simply plug in the formula:

Numbers associated with 43:

We want to see which x value we must choose to get a y value of 43. So, the equation is

a .4y4

hope this !