Topics
>
Precalculus>
Transformations of Functions>
Sketch a Graph using Translations (Shifts)>
Sketch a Graph using Translations (Shifts)Sketch a Graph using Translations (Shifts)
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 4 questions completed
Questions:
- 1
- 2
- 3
- 4
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- Answered
- Review
-
Question 1 of 4
1. Question
Sketch the graph for `y=1/(x+2) + 3` by using `y=1/x`.
Correct
Great Work!
Incorrect
Horizontal and vertical translations of cubed functions are written in the form `y=1/(x-h) + c` where the point `(h,c)` is the intersection point of the asymptotes.To sketch the graph of `y=1/(x+2) + 3`, first find the intersection of the asymptotes and generate a table of values.The formula `y=1/(x-h) + c` when applied to `y=1/x` (can be rewritten as `y=1/(x-(0)) + 0`) gives the intersection point of the asymptotes at `(-2,3)`.Generate a table of values for `y=-x^3` with at least four points.`x` `-2` `-1` `0` `1` `2` `y` `-1/2` `-1` `x` `1` `1/2` Sketch the function `y=1/x` using the table of values and the intersection point of the asymptotes.
Using the formula `y=1/(x-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=1/(x+2) + 3` is `(-2,3)`.
Sketch the curve for `y=1/(x+2) + 3` through the intersection point of its asymptotes `(-2,3)` following the same shape as `y=1/x`.
-
Question 2 of 4
2. Question
Sketch the graph for `y=\sqrt(x+3)-2` by using `y=\sqrt(x)`.
Correct
Great Work!
Incorrect
Horizontal and vertical translations of cubed functions are written in the form `y=\sqrt(x-h)+c` where the point `(h,c)` is the vertex of the function.To sketch the graph of `y=\sqrt(x+3)-2`, first find the vertex and generate a table of values.The formula `y=\sqrt(x-h)+c` when applied to `y=\sqrt(x)` (can be rewritten as `y=\sqrt(x-0)+0`) gives the vertex at `(0,0)`.Generate a table of values for `y=1/x` with at least four points.`x` `0` `1` `2` `4` `6` `y` `0` `1` `1.4` `2` `2.4` Sketch the function `y=1/x` using the table of values and the vertex point.
Using the formula `y=\sqrt(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=\sqrt(x+3)-2` is `(-3,-2)`.
Sketch the curve for `y=\sqrt(x+3)-2` through its vertex point `(-3,-2)` following the same shape as `y=\sqrt(x)`.
-
Question 3 of 4
3. Question
Sketch the graph for `y=(x -2)^3 – 1` by using `y=x^3`.
Correct
Great Work!
Incorrect
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=x^3` (can be rewritten as `y=(x-0)^3+0`) gives the vertex at `(0,0)`.Generate a table of values for `y=-x^3` with at least four points.`x` `-2` `-1` `0` `1` `2` `y` `-8` `-1` `0` `1` `8` Sketch the function `y=x^3` 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=x^3`.
-
Question 4 of 4
4. Question
Sketch the graph for `y=2^(x-1) -2` by using `y=2^x`.
Correct
Great Work!
Incorrect
Horizontal and vertical translations of cubed functions are written in the form `y=2^(x-h) +c` where `y=c` is the asymptote of the function.To sketch the graph of `y=2^(x -1)-2`, first find the asymptote and generate a table of values.The formula `y=2^(x-h) +c` when applied to `y=2^x` (can be rewritten as `2^(x-0) +0`) gives the asymptote at `y=0`.Generate a table of values for `y=2^x` with at least four points.`x` `-2` `0` `1` `2` `3` `y` `1/4` `1` `2` `4` `8` Sketch the function `y=2^x` using the table of values and the asymptote.
Using the formula `y=2^(x-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=2^(x -1)-2` is `y=-2`.
Sketch the curve for `y=2^(x -1)-2` following its asymptote `y=-2` following the same shape as `y=2^x`.
Quizzes
- Vertical Translations (Shifts) 1
- Vertical Translations (Shifts) 2
- Vertical Translations (Shifts) from a Point
- Horizontal Translations (Shifts) 1
- Horizontal Translations (Shifts) from a Point
- Horizontal Translations (Shifts) from a Graph
- Horizontal and Verticals Translations (Shifts) from a Graph
- Sketch a Graph using Translations (Shifts)
- Write the Equation from a Graph
- Write the Equation from Translations (Shifts) 1
- Vertical Dilations (Stretch/Shrink)
- Horizontal Dilations (Stretch/Shrink) 1
- Horizontal Dilations (Stretch/Shrink) 2
- Horizontal Dilations (Stretch/Shrink) – Scale Factor
- Horizontal and Vertical Dilations (Stretch/Shrink) 1
- Horizontal and Vertical Dilations (Stretch/Shrink) 2
- Horizontal and Vertical Dilations (Stretch/Shrink) 3
- Graphing Reflections 1
- Graphing Reflections 2
- Reflection with Rotation
- Combinations of Transformations: Order
- Combinations of Transformations: Coordinates
- Combinations of Transformations: Find Equation 1
- Combinations of Transformations: Find Equation 2
- Combinations of Transformations: Find Equation 3