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Mathematics

2 answers:

Scrat [10]3 years ago

8 0

sorry what?

Step-by-step explanation:

I Don't understand

bezimeni [28]3 years ago

3 0

Answer:

Step-by-step explanation:

I threw them right back at you cause where's the problem???

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dem82 [27]

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3 years ago

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 4

Delicious77 [7]

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: $D = \mathbb{R}$

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 $[a,\infty)$ . To find the minimum, let's start with the "standard" parabola $y=x^2$ , and transform it to the one of this exercise. $y=x^2$ has minimum 0, and thus its range is $[0,\infty)$ . When you multiply it times three, its shape narrows, but the range wont change: $[0,\infty) \to [3\cdot 0,3\cdot \infty) = [0,\infty)$ . Finally, when you subtract 5, you shift everythin down 5 units. This transformation affects the range, since you have $[0,\infty) \to [0-5,\infty-5) = [-5,\infty)$