Question

Sabendo que o zero da função polinominal do 1°grau f(x)=(-5+k)x-(3 k-2) é-4 verifique se f é crescente ou decrescente

Answer 1

Resposta:

Decrescente.

Explicação passo a passo:

f(x) = (–5 + k)x – (3k – 2)

f(–4) = 0

(–5 + k)(–4) – (3k – 2) = 0

20 – 4k – (3k – 2) = 0

20 – 4k – 3k + 2 = 0

22 – 4k – 3k = 0

22 – (4 + 3)k = 0

22 – 7k = 0

22 = 7k

7k = 22

k = 22 / 7

k = (21 + 1) / 7

k = 21 / 7 + 1 / 7

k = 3 + (1/7)

f(x) = (–5 + k)x – (3k – 2)

f(x) = (–5 + 3 + 1/7)x – (3(3 + 1/7) – 2)

f(x) = (–2 + 1/7)x – (9 + 3/7 – 2)

f(x) = (–14/7 + 1/7)x – (7 + 3/7)

f(x) = ((–14 + 1)/7)x – (49/7 + 3/7)

f(x) = (–13/7)x – ((49 + 3)/7)

f(x) = –13x/7 – (52/7)

f(x) = –13x/7 – 52/7

f(x) = (–13x – 52)/7

f(x) = –(13x + 52)/7

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Para f(–4) = 0:

–(13(–4) + 52)/7 = 0

–(–52 + 52)/7 = 0

–(0)/7 = 0

0/7 = 0

0 = 0  ← Verdadeiro.

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f(–3) = –(13(–3) + 52)/7

f(–3) = –(–39 + 52)/7

f(–3) = –(13)/7

f(–3) = –13/7

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Se f(-3) < f(-4) e -3 > -4, então:

f(x) é ≤ 0 para x ≥ –4

É decrescente, pois quanto maior o valor de x, menor o valor de f(x).