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Mathematics
Mathematics
Problem
Consider the piecewise function
p
(
x
)
=
{
a
x
+
b
,
x
<
1
,
a
x
2
,
1
≤
x
<
4
,
b
x
+
3
,
x
≥
4.
p(x)= \begin{cases} ax+b,& x<1,\\ ax^{2},& 1\le x<4,\\ bx+3,& x\ge 4. \end{cases}
p
(
x
)
=
⎩
⎨
⎧
a
x
+
b
,
a
x
2
,
b
x
+
3
,
x
<
1
,
1
≤
x
<
4
,
x
≥
4.
For which ordered pair
(
a
,
b
)
(a,b)
(
a
,
b
)
is
p
p
p
continuous for all real numbers? a)
(
0
,
0
)
\left(0,\,0\right)
(
0
,
0
)
b)
(
3
4
,
0
)
\left(\dfrac{3}{4},\,0\right)
(
4
3
,
0
)
c)
(
1
4
,
0
)
\left(\dfrac{1}{4},\,0\right)
(
4
1
,
0
)
d)
(
3
16
,
0
)
\left(\dfrac{3}{16},\,0\right)
(
16
3
,
0
)
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