Let f x = x 2 . (a) Graph y = f x + k for k = − 4 , 0 , and 2 simultaneously in the same coordinate system . Describe the relationship between the graph of y = f x and the graph of y = f x + k for any real number k . (b) Graph y = f x + h for h = − 4 , 0 , and 2 simultaneously in the same coordinate system. Describe the relationship between the graph of y = f x and the graph of y = f x + h for any real number h .
Let f x = x 2 . (a) Graph y = f x + k for k = − 4 , 0 , and 2 simultaneously in the same coordinate system . Describe the relationship between the graph of y = f x and the graph of y = f x + k for any real number k . (b) Graph y = f x + h for h = − 4 , 0 , and 2 simultaneously in the same coordinate system. Describe the relationship between the graph of y = f x and the graph of y = f x + h for any real number h .
(a) Graph
y
=
f
x
+
k
for
k
=
−
4
,
0
,
and
2
simultaneously in the same coordinate system. Describe the relationship between the graph of
y
=
f
x
and the graph of
y
=
f
x
+
k
for any real number
k
.
(b) Graph
y
=
f
x
+
h
for
h
=
−
4
,
0
,
and
2
simultaneously in the same coordinate system. Describe the relationship between the graph of
y
=
f
x
and the graph of
y
=
f
x
+
h
for any real number
h
.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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