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Is f(x) shifted upward a units?
Yes, if a function ( f(x) ) is shifted upward by ( a ) units, the new function can be expressed as ( f(x) + a ). This transformation moves the entire graph of the function vertically upward without altering its shape. Consequently, every point on the graph of ( f(x) ) increases its ( y )-value by ( a ).
How is the graph of f(x)-3x2-4 different from the graph of f(x)-3x2?
The second graph is shifted upwards by 4 units.
How does graph of y equals x square-1 different from the graph of y equals x square plus 7?
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 is the graph of log x 6 translated from the graph of log x?
The graph of ( \log(x) + 6 ) is a vertical translation of the graph of ( \log(x) ) upwards by 6 units. This means that every point on the graph of ( \log(x) ) is shifted straight up by 6 units, while the shape and orientation of the graph remain unchanged. The domain of the function remains the same, which is ( x > 0 ).
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.
What point lies on the graph of the line of y equals -2x shifted up 4 units?
(4,1)
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.
Is f(x) shifted upward a units?
Yes, if a function ( f(x) ) is shifted upward by ( a ) units, the new function can be expressed as ( f(x) + a ). This transformation moves the entire graph of the function vertically upward without altering its shape. Consequently, every point on the graph of ( f(x) ) increases its ( y )-value by ( a ).
How is the graph of f(x)-3x2-4 different from the graph of f(x)-3x2?
The second graph is shifted upwards by 4 units.
How does graph of y equals x square-1 different from the graph of y equals x square plus 7?
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 is the graph of log x 6 translated from the graph of log x?
The graph of ( \log(x) + 6 ) is a vertical translation of the graph of ( \log(x) ) upwards by 6 units. This means that every point on the graph of ( \log(x) ) is shifted straight up by 6 units, while the shape and orientation of the graph remain unchanged. The domain of the function remains the same, which is ( x > 0 ).
How do you graph cosine functions?
it is the same as a sin function only shifted to the left pi/2 units
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.
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.
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 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
