Question 9 (Worth 1 points)
2 answers:
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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