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What are the characteristics of the graph of the absolute value parent function?
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) ).
Why does the graph of an absolute-value function not extend past the vertex?
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.
What does function of x equals function of -x mean?
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.
What is the difference from a graph that is noted (-) absolute value and ( ) absolute value.?
And stop cheating
Are characteristics of the graph of the absolute value parent function check all that apply?
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.
How do you graph the function of the absolute value of x?
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Which function has a graph that is increasing only?
Absolute Value function
What is the corner point of a graph of an absolute value equation?
It is sometimes the point where the value inside the absolute function is zero.
What letter of the alphabet would an absolute value function look like?
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.
What do you call a V-shape on a graph?
That is a result of an absolute value equation. So an Absolute Value Graph
What is an absolute function?
The absolute value function returns the absolute value of a number.
Which statement holds true for absolute value functions The absolute value determines the direction in which the graph opens. The coefficient determines the line along which the graph is symmetrical.?
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.
Can the graph of an absolute value be negative?
No.
Why does the graph of an absolute-value function not extend past the vertex?
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.
How do you do absolute value functions on your Casio fx-9750GII Graphing Calculator?
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.
What is a function whose rule contains absolute value expressions?
An absolute-value function
What does function of x equals function of -x mean?
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.
