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Byju's Answer
Standard XII
Mathematics
Graphical Interpretation of Differentiability
Identify the ...
Question
Identify the graph of the polynomial function
f
f
(
x
)
=
x
2
+
2
x
−
3
A
graph a
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B
graph b
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C
graph c
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D
graph d
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Solution
The correct option is
A
graph a
Let
y
=
x
2
+
2
x
−
3
The graph of
f
(
x
)
in this example is the graph of
y
=
x
2
+
2
x
−
3
. It is easy to generate points on the graph.
Choose a value for the first coordinate, then evaluate
y
at that number to find the second coordinate.
The several values for
x
and the function
y
evaluated at those numbers.
If
x
=
0
, then
y
=
(
0
)
2
+
2
(
0
)
−
3
=
0
+
0
−
3
=
−
3
implies the point is
(
0
,
−
3
)
.
If
x
=
1
, then
y
=
(
1
)
2
+
2
(
1
)
−
3
=
1
+
2
−
3
=
0
implies the point is
(
1
,
0
)
.
If
x
=
−
1
, then
y
=
(
−
1
)
2
+
2
(
−
1
)
−
3
=
1
−
2
−
3
=
−
4
implies the point is
(
−
1
,
−
4
)
.
Hence, the graph of the function is shown above.
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