0
What else can I help you with?
What of the following is a key property of the absolute value parent function?
It’s vertex is not at the origin
Which of the following is a key property of the absolute value parent function?
Its vertex is not at the origin
What is the corner point of the graph of an absolute value equation called?
vertex
Can absolute value functions be onto?
Yes, if the range is the non-negative reals.
The greatest integer function and absolute value function are both examples of functions that can be defined as what?
Both the Greatest Integer Function and the Absolute Value Function are considered Piece-Wise Defined Functions. This implies that the function was put together using parts from other functions.
What of the following is a key property of the absolute value parent function?
It’s vertex is not at the origin
Which of the following is a key property of the absolute value parent function?
Its vertex is not at the origin
What are two absolute value equations that share a vertex?
In math a normal absolute value equations share a vertex.
What function is the same as the attribute of the absolute value parent function?
The attribute of the absolute value parent function, ( f(x) = |x| ), is its vertex, which is located at the point (0, 0). This function is characterized by its V-shaped graph, indicating that it reaches a minimum value at the vertex. The absolute value function is even, meaning it is symmetric about the y-axis. Its key feature is that it outputs non-negative values for all real inputs.
Is the y intercept the same as a absolute value parent function?
No, the y-intercept is not the same as the absolute value parent function. The absolute value parent function, represented as ( f(x) = |x| ), has a vertex at the origin (0, 0), which serves as its y-intercept. While the absolute value function does have a specific y-intercept, the term "y-intercept" generally refers to the point where any function crosses the y-axis, which can vary depending on the function in question.
What statement holds true for absolute value functions?
Absolute value functions output the non-negative distance of a number from zero on the number line. This means that for any real number ( x ), the absolute value ( |x| ) is always greater than or equal to zero. Additionally, the graph of an absolute value function forms a "V" shape, with its vertex at the origin (0,0) if centered there, and it is symmetric about the y-axis.
Which parent functions has a domain and range of all real numbers excluding the origin?
y = 1/x
How are linear and absolute value functions similar?
Linear and absolute value functions are similar in that both types of functions can be expressed in a mathematical form and represent straight lines on a graph. They both exhibit a consistent rate of change: linear functions have a constant slope, while absolute value functions have a V-shaped graph that consists of two linear segments meeting at a vertex. Additionally, both functions can be used to model real-world situations, though their behaviors differ in how they respond to changes in their input values.
What is the corner point of the graph of an absolute value equation called?
vertex
A key property of the absolute-value parent function?
A key property of the absolute-value parent function, ( f(x) = |x| ), is that it is V-shaped and symmetric about the y-axis. It has a vertex at the origin (0, 0) and its output is always non-negative, meaning ( f(x) \geq 0 ) for all ( x ). The function increases linearly for ( x > 0 ) and decreases linearly for ( x < 0 ). This characteristic makes it a fundamental example in understanding piecewise functions and transformations.
If you shift the absolute value parent function F(x) x right 9 units what is the equation of the new function?
To shift the absolute value parent function ( F(x) = |x| ) right by 9 units, you replace ( x ) with ( x - 9 ). Therefore, the equation of the new function becomes ( F(x) = |x - 9| ). This transformation moves the vertex of the absolute value function from the origin to the point (9, 0).
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.
