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How To Identify the vertical and horizontal shifts from the formula. The vertical shift results from a constant added to the output. Move the graph up for a positive constant and down for a negative constant. The horizontal shift results from a constant added to the input. ... Apply the shifts to the graph in either order.
Horizontal Shift Equation The equation indicating a horizontal shift to the left is y = f(x + a). The equation indicating a horizontal shift to the right is y = f(x - a). For example, in order to shift the graph of y = x^2 + 2 to the right 4 places, the equation must be written y = (x-4)^2 +2.
An equation can be shifted vertically by changing the constant, that is, the number that stands alone after the x-value. For example, in order to shift the linear equation y = x - 2 vertically, change the "-2" by adding or subtracting. A positive change, adding 3 to the constant -2, will shift the graph up 3 units.
Horizontal shifts are inside changes that affect the input (x-) axis values and shift the function left or right. Combining the two types of shifts will cause the graph of a function to shift up or down and right or left.
Horizontal shifts are inside changes that affect the input (x-) axis values and shift the function left or right. Combining the two types of shifts will cause the graph of a function to shift up or down and right or left.

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Horizontal Shifts Adding a value to the x variable shifts a graph to the left, and subtracting a value from the x variable shifts it to the right. For example, if f(x) = x, then a horizontal shift will take place at f(x + 1), moving the line one place to the left.
How To Identify the vertical and horizontal shifts from the formula. The vertical shift results from a constant added to the output. Move the graph up for a positive constant and down for a negative constant. The horizontal shift results from a constant added to the input. ... Apply the shifts to the graph in either order.
Formally: given a function f(x), and a constant a > 0, the function g(x) = f(x - a) represents a horizontal shift a units to the right from f(x). The function h(x) = f(x + a) represents a horizontal shift a units to the left.
To help you visualize the concept of a vertical shift, consider that y=f(x). Therefore, f(x)+k is equivalent to y+k. Every unit of y is replaced by y+k, so the y-value increases or decreases depending on the value of k. The result is a shift upward or downward.
Vertical shifts are outside changes that affect the output (y\u2212) axis values and shift the function up or down. Horizontal shifts are inside changes that affect the input (x\u2212) axis values and shift the function left or right.

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