HELPPPP. SOMEONE HELP PLEASE

Mathematics

2 answers:

nata0808 [166]3 years ago

3 0

Answer:

a) Domain: All real numbers

b) Domain: -4<x<=4

a) Range: All real numbers greater than 2

b) Range: 0<=y<=4

Step-by-step explanation:

Domain is the possible x values

Range is the possible y values

Open circle means not included

Close circle means included

daser333 [38]3 years ago

3 0

Answer: a) Domain: x = (-∞, ∞) b) Domain x = (-4, 4]

Range y = [2, ∞) Range y = [0, 4]

<u>Step-by-step explanation:</u>

Domain represents the x-values. Range represents the y-values.

a) the graph doesn't end so every x-value is possible

x = All Real Numbers x = (-∞, ∞)

The lowest y-value (minimum) is at y = 2. All other y-values are greater than that. y ≥ 2 y = [2, ∞)

b) The graph starts at x = -4 with an open dot so it doesn't include -4. It ends at x = +4 with a closed dot so it does include +4.

-4 < x ≤ 4 x = (-4, 4]

The lowest y-value (minimum) is at y = 0. All other y-values are greater than that up to y = 4. 0 ≤ y ≤ 4 y = [0, 4]

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. Andrew made an error in determining the polynomial equation of smallest degree whose roots are 3, 2+2i

KIM [24]

Answer:

Error of Andrew: Made incorrect factors from the roots

Step-by-step explanation:

Roots of the polynomial are: 3, 2 + 2i, 2 - 2i. According to the factor theorem, if a is a root of the polynomial P(x), then (x - a) is a factor of P(x). According to this definition:

(x - 3) , (x - (2 + 2i)) , (x - (2 - 2i)) are factors of the required polynomial.

Simplifying the brackets, we get:

(x - 3), (x - 2 - 2i), (x - 2 + 2i) are factors of the required polynomial.

This is the step where Andrew made the error. The factors will always be of the form (x - a) , not (x + a). Andrew wrote the complex factors in form of (x + a) which resulted in the wrong answer.

So, the polynomial would be:

$(x - 3)(x - 2 - 2i)(x - 2+2i)=0\\\\ (x-3)(x^{2}-2x+2xi-2x+4-4i-2xi+4i-4i^{2})=0\\\\ (x-3)(x^{2}-4x+4+4)=0\\\\ (x-3)(x^{2}-4x+8)=0\\\\ x^{3}-4x^{2}+8x-3x^{2}+12x-24=0\\\\ x^{3}-7x^{2}+20x-24=0$