Horizontal and vertical translations of cubed functions are written in the form y=1x-h+cy=1x−h+c where the point (h,c)(h,c) is the intersection point of the asymptotes.
To sketch the graph of y=1x+2+3y=1x+2+3, first find the intersection of the asymptotes and generate a table of values.
The formula y=1x-h+cy=1x−h+c when applied to y=1xy=1x (can be rewritten as y=1x-(0)+0y=1x−(0)+0) gives the intersection point of the asymptotes at (-2,3)(−2,3).
Generate a table of values for y=-x3y=−x3 with at least four points.
xx
-2−2
-1−1
00
11
22
yy
-12−12
-1−1
xx
11
1212
Sketch the function y=1xy=1x using the table of values and the intersection point of the asymptotes.
Using the formula y=1x-h+cy=1x−h+c for horizontal and vertical translations and remembering that the point (h,c)(h,c) is the intersection point of the asymptotes, the intersection point of the asymptotes for y=1x+2+3y=1x+2+3 is (-2,3)(−2,3).
Sketch the curve for y=1x+2+3y=1x+2+3 through the intersection point of its asymptotes (-2,3)(−2,3) following the same shape as y=1xy=1x.
Question 2 of 4
2. Question
Sketch the graph for y=√x+3-2y=√x+3−2 by using y=√xy=√x.
Horizontal and vertical translations of cubed functions are written in the form y=√x-h+cy=√x−h+c where the point (h,c)(h,c) is the vertex of the function.
To sketch the graph of y=√x+3-2y=√x+3−2, first find the vertex and generate a table of values.
The formula y=√x-h+cy=√x−h+c when applied to y=√xy=√x (can be rewritten as y=√x-0+0y=√x−0+0) gives the vertex at (0,0)(0,0).
Generate a table of values for y=1xy=1x with at least four points.
xx
00
11
22
44
66
yy
00
11
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.
