Horizontal and vertical translations of cubed functions are written in the form y=1x−h+c where the point (h,c) is the intersection point of the asymptotes.
To sketch the graph of y=1x+2+3, first find the intersection of the asymptotes and generate a table of values.
The formula y=1x−h+c when applied to y=1x (can be rewritten as y=1x−(0)+0) gives the intersection point of the asymptotes at (−2,3).
Generate a table of values for y=−x3 with at least four points.
x
−2
−1
0
1
2
y
−12
−1
x
1
12
Sketch the function y=1x using the table of values and the intersection point of the asymptotes.
Using the formula y=1x−h+c for horizontal and vertical translations and remembering that the point (h,c) is the intersection point of the asymptotes, the intersection point of the asymptotes for y=1x+2+3 is (−2,3).
Sketch the curve for y=1x+2+3 through the intersection point of its asymptotes (−2,3) following the same shape as y=1x.
Horizontal and vertical translations of cubed functions are written in the form y=√x−h+c where the point (h,c) is the vertex of the function.
To sketch the graph of y=√x+3−2, first find the vertex and generate a table of values.
The formula y=√x−h+c when applied to y=√x (can be rewritten as y=√x−0+0) gives the vertex at (0,0).
Generate a table of values for y=1x with at least four points.
x
0
1
2
4
6
y
0
1
1.4
2
2.4
Sketch the function y=1x using the table of values and the vertex point.
Using the formula y=√x−h+c for horizontal and vertical translations and remembering that the point (h,c) is the vertex of the function, the vertex point for y=√x+3−2 is (−3,−2).
Sketch the curve for y=√x+3−2 through its vertex point (−3,−2) following the same shape as y=√x.
Horizontal and vertical translations of cubed functions are written in the form y=(x−h)3+c where the point (h,c) is the vertex of the function.
To sketch the graph of y=(x−2)3−1, first find the vertex and generate a table of values.
The formula y=(x−h)3+c when applied to y=x3 (can be rewritten as y=(x−0)3+0) gives the vertex at (0,0).
Generate a table of values for y=−x3 with at least four points.
x
−2
−1
0
1
2
y
−8
−1
0
1
8
Sketch the function y=x3 using the table of values and the vertex point.
Using the formula y=(x−h)3+c for horizontal and vertical translations and remembering that the point (h,c) is the vertex of the function, the vertex point for y=(x−2)3−1 is (2,−1).
Sketch the curve for y=(x−2)3−1 through its vertex point (2,−1) following the same shape as y=x3.
Horizontal and vertical translations of cubed functions are written in the form y=2x−h+c where y=c is the asymptote of the function.
To sketch the graph of y=2x−1−2, first find the asymptote and generate a table of values.
The formula y=2x−h+c when applied to y=2x (can be rewritten as 2x−0+0) gives the asymptote at y=0.
Generate a table of values for y=2x with at least four points.
x
−2
0
1
2
3
y
14
1
2
4
8
Sketch the function y=2x using the table of values and the asymptote.
Using the formula y=2x−h+c for horizontal and vertical translations and remembering that the point y=c is the equation of the asymptote of the function, the asymptote for y=2x−1−2 is y=−2.
Sketch the curve for y=2x−1−2 following its asymptote y=−2 following the same shape as y=2x.
