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2.9 C) Translations Parallel to the x-axis – Part 2
2.9 C) Translations Parallel to the x-axis – Part 2
The content in this section builds on the content that was discussed in the previous section. Before working through this section, make sure that you have covered the content in the previous section (click here to be taken back to the previous section).
The Rules
The form for translations that are parallel to the x axis is:
The form for translations that are parallel to the x axis is:
And the rules are:
- A positive value for a will move the original curve to left
- A negative value for a will move the original curve to the right
Example 1
The graph below shows the function g(x).
The graph below shows the function g(x).
There are two points shown on the graph; point A and point B. Point A has the coordinates (-3, 4) and point B has the coordinates (2, -5).
For the two translations below, quickly sketch the new graph and show what the new coordinates are for point A and point B.
I am just going to use the rule to find out what the coordinates are for A and B for each of the two transformations above. The rule states that we take the value for a (the number that is either added or subtracted from x inside of the bracket) away from the x coordinate of the point that we are looking for.
Part 1
The first part involves the translation g(x – 5). The value of a in this translation is -5, which means that the curve will be moving 5 towards the right (remember a negative value for a results in the curve moving towards the right).
We can find the coordinates for point A and point B on the translated curve by taking -5 away from the x coordinates for point A and point B. The coordinates for point A are (-3, 4). The working for finding point A on the translated curve g(x – 5) is:
For the two translations below, quickly sketch the new graph and show what the new coordinates are for point A and point B.
- g(x – 5)
- g(x + 4)
I am just going to use the rule to find out what the coordinates are for A and B for each of the two transformations above. The rule states that we take the value for a (the number that is either added or subtracted from x inside of the bracket) away from the x coordinate of the point that we are looking for.
Part 1
The first part involves the translation g(x – 5). The value of a in this translation is -5, which means that the curve will be moving 5 towards the right (remember a negative value for a results in the curve moving towards the right).
We can find the coordinates for point A and point B on the translated curve by taking -5 away from the x coordinates for point A and point B. The coordinates for point A are (-3, 4). The working for finding point A on the translated curve g(x – 5) is:
Point A on the translated curve is (2, 4).
The coordinates of point B are (2, -5). We find the coordinates for point B on the translated curve by taking -5 from the x coordinate of point B. The working is shown below:
The coordinates of point B are (2, -5). We find the coordinates for point B on the translated curve by taking -5 from the x coordinate of point B. The working is shown below:
We now have both point A and point B on the translated curve; point A is (2, 4) and point B is (7, -5). Both of these curves have been sketched on the graph below; g(x) is in blue and g(x – 5) is in green.
Part 2
Let’s now find the coordinates for the second translation, which is g(x + 4). The value of a is 4 and this means that the curve will move 4 to the left.
We can find the coordinates of A and B by taking the value of a off of the x coordinates for point A and point B. The working is shown below:
Let’s now find the coordinates for the second translation, which is g(x + 4). The value of a is 4 and this means that the curve will move 4 to the left.
We can find the coordinates of A and B by taking the value of a off of the x coordinates for point A and point B. The working is shown below:
Point A on the translated graph is (-7, 4) and point B is (-2, -5). The original curve and the translated curve have been sketched on the graph below; the function g(x) is in blue and the function g(x + 4) is in orange.
End Note
The key thing to remember is that a positive value for a (a number being added to the x inside the bracket) will move the graph towards the left by the value that is in the bracket. A negative value for a (a number being taken away from the x inside the bracket) will move the graph to the right. The second thing to remember is that we obtain the coordinates for a particular point by taking the value of a from the x coordinate for the point that we are trying to find on the translated curve. The rule is shown below:
The key thing to remember is that a positive value for a (a number being added to the x inside the bracket) will move the graph towards the left by the value that is in the bracket. A negative value for a (a number being taken away from the x inside the bracket) will move the graph to the right. The second thing to remember is that we obtain the coordinates for a particular point by taking the value of a from the x coordinate for the point that we are trying to find on the translated curve. The rule is shown below: