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Q: What point lies on the graph of the line of y equals -2x shifted up 4 units?
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Which point lies on the graph of the line of y equals -2y shifted up 4 units?

y = -y implies the first line is y = 0 or the x axis. Shifted up 4 units, it becomes the line y = 4.

Which is the exponential form of log 8 x equals 3?

The graph of is shifted 3 units down and 2 units right. Which equation represents the new graph?

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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The second graph is shifted upwards by 4 units.

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They're exactly the same shape and size, but every point on the graph of the first one is 8 units directly below the corresponding point on the graph of the second one.

How do you graph cosine functions?

it is the same as a sin function only shifted to the left pi/2 units

In the vertex form of a quadratic function y equals a the quantity of x-b squared plus c what does the b tell you about the graph?

The standard form of the quadratic function in (x - b)2 + c, has a vertex of (b, c). Thus, b is the units shifted to the right of the y-axis, and c is the units shifted above the x-axis.

How does adding a constant c to x in the parent graph y equals x affect the graph?

If y = f(x), then y = f(x + c) is the same graph shifted c units to the left (or right if c is negative) along the x-axis For y = x, by changing x to x + c, the above shift is indistinguishable from shifting the graph c units up (or down if c is negative) the y-axis.

Which statement correctly describes the graph of g(x) if g(x) f(x - 6)?

The graph of g(x) is the graph of f(x) shifted 6 units in the direction of positive x.

What happens to the graph of y equals x when the equation changes to y equals x - 9?

The graph shifts downward (negative y) by 9 units.

What is the effect on the graph of the equation y equals x2 plus 2 when it is changed to y equals x2 - 4?

the graph is moved down 6 units

Graph -5 on the number line?

Go what equals 5 units to the left