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Instructions
Count the number of units the graph of the square root is vertically removed from the origin point, (0,0). If the graph originates above (0, 0), then a constant number has been added to the square root function. If the graph originates below (0, 0), then a constant number has been subtracted from the square root function. For example, the function f(x) = √x + 4 indicates that the square root graph is shifted 4 units up the y-axis.
Count the number of units the graph of the square root is horizontally removed from the point (0, 0). If the graph is shifted a number of units to the left of the origin point, then a constant number has been added to the x-value of the function. If the graph is shifted a number of units to the right of the origin point, then a constant number has been subtracted from the x-value of the function. For example, the function √(x + 4) indicates that the square root graph is shifted 4 units to the left of its initial position.
Compare the graph of the basic square root function, f(x) = √x, to the graph of the graph of the transformed square root function. If the the graph of the transformed square root function is steeper (meaning it grows faster) than the basic function, this indicates that either the entire function has be multiplied by a constant number, or the x-value within the function has been raised to a power. It is virtually impossible to guess the degree of this constant multiplier simply by looking at the graph.
Note whether the graph of the square root has been flipped about the x-axis or y-axis. The entire function has been multiplied by a negative constant if the graph has been flipped "upside down." The x-value inside the function has been multiplied by a negative constant if the graph is reflected about the y-axis.