The absolute value of a function changes the original function by ensuring that any negative y values will in essence be positive. For instance, the function y = absolute value (x) will yield the value +1 when x equals -1. Graphically, this function will look like a "V".
The graph of the absolute value parent function, ( f(x) = |x| ), has a distinct V-shape that opens upwards. It is symmetric about the y-axis, meaning it is an even function. The vertex of the graph is at the origin (0, 0), and the graph consists of two linear pieces: one with a slope of 1 for ( x \geq 0 ) and another with a slope of -1 for ( x < 0 ). The function is continuous and has a range of ( [0, \infty) ).
The graph of an absolute-value function does not extend past the vertex because the vertex represents the minimum (or maximum, in the case of a downward-opening parabola) point of the graph. The absolute value ensures that all output values are non-negative (or non-positive), meaning that as you move away from the vertex in either direction, the values will either increase or decrease but never go below the vertex value. Consequently, the graph is V-shaped and reflects this property, making it impossible for the graph to extend beyond the vertex in the negative direction.
It means that the value of the function at any point "x" is the same as the value of the function at the negative of "x". The graph of the function is thus symmetrical around the y-axis. Examples of such functions are the absolute value, the cosine function, and the function defined by y = x2.
And stop cheating
The graph of the absolute value parent function, ( f(x) = |x| ), has a V-shape with its vertex at the origin (0, 0). It is symmetric about the y-axis, indicating that it is an even function. The graph consists of two linear segments that extend infinitely in the positive y-direction, with a slope of 1 for ( x \geq 0 ) and a slope of -1 for ( x < 0 ). Additionally, it never dips below the x-axis, as absolute values are always non-negative.
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Absolute Value function
It is sometimes the point where the value inside the absolute function is zero.
The letter of the alphabet of the absolute value function looks like a V. For this reason, it is a popular graph at Villanova University.
That is a result of an absolute value equation. So an Absolute Value Graph
The absolute value function returns the absolute value of a number.
Neither statement is true. The graph of the absolute value of a function which is always non-negative will be the same as that of the original function and this need not open in any direction. Also, the graph of y = abs[x*(x-1)*(x+2)] is not symmetrical so there is no coefficient which will determine a line of symmetry.
No.
The graph of an absolute-value function does not extend past the vertex because the vertex represents the minimum (or maximum, in the case of a downward-opening parabola) point of the graph. The absolute value ensures that all output values are non-negative (or non-positive), meaning that as you move away from the vertex in either direction, the values will either increase or decrease but never go below the vertex value. Consequently, the graph is V-shaped and reflects this property, making it impossible for the graph to extend beyond the vertex in the negative direction.
To graph absolute value functions on your Casio fx-9750GII, first, press the "MODE" button and select "Graph" mode. Then, input the absolute value function using the notation "abs(x)" or by using the "SHIFT" key followed by the "x" key to access the absolute value function. After entering your equation (e.g., y = abs(x - 2)), press the "EXE" button and then the "F1" key to graph it. You can adjust the viewing window if needed by pressing the "VIEW" button.
An absolute-value function
It means that the value of the function at any point "x" is the same as the value of the function at the negative of "x". The graph of the function is thus symmetrical around the y-axis. Examples of such functions are the absolute value, the cosine function, and the function defined by y = x2.