Y = 2 The graph is a horizontal line passing through the point Y=2 on the Y=axis. The line is parallel to the X-axis, and exactly 2 units above it everywhere.
First, reflect the graph of y = x² in the x-axis (line y = 0) to obtain the graph of y = -x²; then second, shift it 3 units up to obtain the graph of y = -x² + 3.
To translate the graph y = x to the graph of y = x - 6, shift the graph of y = x down 6 units.
y = -y implies the first line is y = 0 or the x axis. Shifted up 4 units, it becomes the line y = 4.
The graph of is shifted 3 units down and 2 units right. Which equation represents the new graph?
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.
The second graph is shifted upwards by 4 units.
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.
it is the same as a sin function only shifted to the left pi/2 units
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.
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.
The graph of g(x) is the graph of f(x) shifted 6 units in the direction of positive x.
The graph shifts downward (negative y) by 9 units.
the graph is moved down 6 units
Go what equals 5 units to the left