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National High School Mathematics League
1983 National High School Mathematics League
5
Twice Function
Twice Function
Source: 1983 National High School Mathematics League, Exam One, Problem 5
February 21, 2020
function
Problem Statement
f
(
x
)
=
a
x
2
−
c
f(x)=ax^2-c
f
(
x
)
=
a
x
2
−
c
. If
−
4
≤
f
(
1
)
≤
−
1
,
−
z
≤
f
(
2
)
≤
5
-4\leq f(1)\leq -1,-z\leq f(2)\leq 5
−
4
≤
f
(
1
)
≤
−
1
,
−
z
≤
f
(
2
)
≤
5
, then
(A)
7
≤
f
(
3
)
≤
26
(B)
−
4
≤
f
(
3
)
≤
15
(C)
−
1
≤
f
(
3
)
≤
23
(D)
−
28
3
≤
f
(
3
)
≤
35
3
\text{(A)}7\leq f(3)\leq26\qquad\text{(B)}-4\leq f(3)\leq15\qquad\text{(C)}-1\leq f(3)\leq23\qquad\text{(D)}-\frac{28}{3}\leq f(3)\leq\frac{35}{3}
(A)
7
≤
f
(
3
)
≤
26
(B)
−
4
≤
f
(
3
)
≤
15
(C)
−
1
≤
f
(
3
)
≤
23
(D)
−
3
28
≤
f
(
3
)
≤
3
35
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