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Q: What If H(x) 4x2 - 16 were shifted 9 units to the right and 1 down what would the new equation be?
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Is f(x) shifted downward a units?

To shift a funcion (or its graph) down "a" units, you subtract "a" from the function. For example, x squared gives you a certain graph; "x squared minus a" will give you the same graph, but shifted down "a" units. Similarly, you can shift a graph upwards "a" units, by adding "a" to the function.


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Write an equation for the horizontal translation of y - x?

For a start, you would need an initial equation. A horizontal translation of ANY equation can be achieved by replacing every ocurrence of "x" with "x - a", where "a" is the amount you want to move the graph to the right. For example, replacing every ocurrence of "x" by "x - 10" will move your graph 10 units to the right.


Where would y equals x - 3 be on a graph?

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Graph the equation y equals 2x plus 1?

So, if we see the basic equation y=mx+b, we see that m=2, and b=1. If you look closely, this is basic rotation and translation of the original graph. First, I would translate the "mother graph" (y=mx) and then translate one up. Then, we would rotate the graph to the right two units.