Shifting or Translating Curves along Axes (3.16.2)

Question 1

• Shifting up or down on a graph is a matter of adding or subtracting a value to the expression that gives you the y-values.

Answer 1

• Shifting up or down on a graph is a matter of adding or subtracting a value to the expression that gives you the y-values.

Question 2

• Shifting sideways on a graph is a matter of adding or subtracting within parentheses with the x. Remember shifts move
opposite to the signs added in these x-expressions.

Answer 2

• Shifting sideways on a graph is a matter of adding or subtracting within parentheses with the x. Remember shifts move
opposite to the signs added in these x-expressions.

Question 3

• Shift carefully. When you add to y, go high. When you add to x, go west.

Answer 3

• Shift carefully. When you add to y, go high. When you add to x, go west.

Question 4

Consider the example here: graph g(x) = x
2 + 1.
In this case, +1 was added to the expression used to derive
the y-values.
So, the entire curve shifted up one unit on the axes.
This happens because for every point (x, y) on the original
curve there exists a point (x, y +1) on the new curve.
In this example, –3 is added to the expression used to derive
the y-values.
The result is that every y is reduced by 3 and the entire curve
drops three units on the axes.
In generic terms, for every point (x, y) on the original curve
there exists a point (x, y – 3) on the new curve.
Shifting sideways is a little more complicated. The value to
shift must accompany the x within the parentheses. By doing
this, you are really changing the value of x.
Notice that when you add a positive number to x, the graph
shifts to the negative, i.e., to the left.
In this example, (x + 2)2
shifts the curve 2 units to the left.
Once again, here is the basic parabola with its vertex at the
origin.
In this example, (x – 1)2
shifts the curve 1 unit to the right.
When you add a negative number to x, the graph shifts to the
positive, i.e., to the right.

Answer 4

Consider the example here: graph g(x) = x
2 + 1.
In this case, +1 was added to the expression used to derive
the y-values.
So, the entire curve shifted up one unit on the axes.
This happens because for every point (x, y) on the original
curve there exists a point (x, y +1) on the new curve.
In this example, –3 is added to the expression used to derive
the y-values.
The result is that every y is reduced by 3 and the entire curve
drops three units on the axes.
In generic terms, for every point (x, y) on the original curve
there exists a point (x, y – 3) on the new curve.
Shifting sideways is a little more complicated. The value to
shift must accompany the x within the parentheses. By doing
this, you are really changing the value of x.
Notice that when you add a positive number to x, the graph
shifts to the negative, i.e., to the left.
In this example, (x + 2)2
shifts the curve 2 units to the left.
Once again, here is the basic parabola with its vertex at the
origin.
In this example, (x – 1)2
shifts the curve 1 unit to the right.
When you add a negative number to x, the graph shifts to the
positive, i.e., to the right.