Graph f(x)=|x−2|+3 .
1 answer:
f(x) + n - translate the graph of f(x) n units up
f(x) - n - translate the graph of f(x) n units down
f(x + n) - translate the graph of f(x) n units left
f(x - n) - translate the graph of f(x) n units right
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f(x) = |x - 2| + 3
g(x) = |x| → f(x - 2) + 3 = |x - 2| + 3
Translate the graph of g(x) 2 units right and 3 units up.
g(x) = |x|
for x = -2 → y = |-2| = 2 → (-2, 2)
for x = 0 → y = |0| = 0 → (0, 0)
for x = 2 → y = |2| = 2 → (2, 2)
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Answer:
a) 8, multiplicity 2; 8, multiplicity 3
Step-by-step explanation:
Remember that a is a zero of the polynomial f(x) if f(a)=0 and has multiplicity n if the termn (x-a) is n times in the factorization of f(x).
We have that
Observe that
1.
and (x+8) appear two times in the factorization of f(x). Then -8 is a zero of f(x) with multiplicity 2.
2.
and and (x - 8) appear three times in the factorization of f(x). Then 8 is a zero of f(x) with multiplicity 3.
Since f(x) has degree 5 and the sum of the multiplicities is 5 then f(x) hasn't more zeros.