y = f (x) + 6 1) Generate a Table of Values for y = x2 + 6 The values shown in yellow are used for the original graph. The values shown in blue are used for the new graph. 2) Plot the Graph of the Original Function and the New Function 3) Compare the Graphs The original graph is shown in blue, and the new graph is shown in green. How does it compare? It appears that the new graph is six units higher than the original graph. Its shape is still the same. |
y = f(x) - 2 1) Generate a Table of Values for y = x2 - 2 The values shown in yellow are used for the original graph. The values shown in blue are used for the new graph. 2) Plot the Graph of the Original Function and the New Function 3) Compare the Graphs The original graph is shown in blue, and the new graph is shown in red. How does it compare? It appears that the new graph is two units lower than the original graph. Its shape is still the same. |
Why does this happen?
When we evaluate the
new function, we first evaluate f(x) at any value of x. In this case,
the value of f(x) remains the same for that x value. Then by adding on
the constant term at the end of the equation, we add c to f(x). This
means each value of x has the value of f(x) at the point, with an
additional c added on to it.
On To Scaling
Y-Coordinates
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the Introduction