Shifting Curves along Axes (3.16.1) Flashcards
• Shifting a graph up is a matter of adding a value to the expression that produces the y-values. Likewise, shifting a graph down is a matter of subtracting a value from the same expression.
• Shifting a graph up is a matter of adding a value to the expression that produces the y-values. Likewise, shifting a graph down is a matter of subtracting a value from the same expression.
• Shifting a graph to the left on the axes is a matter of adding a value so that the x-values increase, (x + c). Likewise, shifting a graph to the right is a matter of subtracting a value so that the x-values decrease, (x – c).
• Shifting a graph to the left on the axes is a matter of adding a value so that the x-values increase, (x + c). Likewise, shifting a graph to the right is a matter of subtracting a value so that the x-values decrease, (x – c).
• Symmetry means that half the graph is the exact mirror image of the other half.
• Symmetry means that half the graph is the exact mirror image of the other half.
Moving a graph up on the axes involves adding a value to the expression that produces the y-values. In this example, f (x) = x^2 is shown graphed with its vertex at the origin. Then, +1 is added to the expression for f (x), or y. As a result, the entire curve lifts up one unit on the axes. This change is shown by the upper curve on the graph.
Moving a graph up on the axes involves adding a value to the expression that produces the y-values. In this example, f (x) = x^2 is shown graphed with its vertex at the origin. Then, +1 is added to the expression for f (x), or y. As a result, the entire curve lifts up one unit on the axes. This change is shown by the upper curve on the graph.
Moving a graph down on the axes involves subtracting a
value from the expression that produces the y-values.
In this example, f (x) = x^2 is shown graphed with its vertex at the origin. Then, –1 is added to the expression for f (x) so that the entire curve shifts down one unit on the axes. This change is shown by the lower curve on the graph.
Moving a graph down on the axes involves subtracting a
value from the expression that produces the y-values.
In this example, f (x) = x^2 is shown graphed with its vertex at the origin. Then, –1 is added to the expression for f (x) so that the entire curve shifts down one unit on the axes. This change is shown by the lower curve on the graph.
Movement sideways on a graph involves changing x-values without changing y-values. You generally do it by adding or subtracting some value to the x within parentheses so that the manipulations of the equation include it with the x-values. NOTE: The curve moves sideways opposite to the sign of the number added to the x-expression. Symmetry means that you can cut a curve in half, flip one half over on top of the other one, and they will exactly match. Symmetry also means that if you put a mirror at the vertex of a curve, the curve that appears in the mirror will exactly match the portion of the graph that the mirror is covering up.
Movement sideways on a graph involves changing x-values without changing y-values. You generally do it by adding or subtracting some value to the x within parentheses so that the manipulations of the equation include it with the x-values. NOTE: The curve moves sideways opposite to the sign of the number added to the x-expression. Symmetry means that you can cut a curve in half, flip one half over on top of the other one, and they will exactly match. Symmetry also means that if you put a mirror at the vertex of a curve, the curve that appears in the mirror will exactly match the portion of the graph that the mirror is covering up.
