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How does the graph of relate to its parent function?
The graph of a function can relate to its parent function through transformations such as translations, reflections, stretches, or compressions. For example, if the parent function is a quadratic ( f(x) = x^2 ), a transformed function like ( g(x) = (x - 2)^2 + 3 ) represents a horizontal shift to the right by 2 units and a vertical shift up by 3 units. These transformations affect the graph's position and shape while maintaining the overall characteristics of the parent function.
What must be true about the coefficient of a linear function if that function experiences a vertical stretch of the parent function?
For a linear function to experience a vertical stretch of the parent function ( f(x) = mx + b ), the coefficient ( m ) (the slope) must be greater than 1. A vertical stretch means that the output values of the function are scaled up, making the graph steeper compared to the original. Thus, if the original function has a slope ( m ), the transformed function will have a slope of ( k \cdot m ) where ( k > 1 ).
What is the quadratic parent function?
The quadratic parent function is represented by the equation ( f(x) = x^2 ). It is a basic polynomial function that forms a parabolic graph opening upwards, with its vertex at the origin (0, 0). The function is symmetrical about the y-axis and has a minimum value of 0 at the vertex. The shape of the parabola is defined by its standard form, which can be transformed through vertical and horizontal shifts, stretches, or reflections.
What is the definition of parent function?
When a function is nested inside another function, the outer one is the parent, the inner is the child.
Is a parent function a parabola?
A parent function is a basic function that serves as a foundation for a family of functions. The quadratic function, represented by ( f(x) = x^2 ), is indeed a parent function that produces a parabola when graphed. However, there are other parent functions as well, such as linear functions and cubic functions, which produce different shapes. Therefore, while the parabola is one type of parent function, it is not the only one.
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 the linear parent function?
Please don't write "the following" if you don't provide a list. We can't guess what you are looking at.
Which of the following is a key property of the absolute value parent function?
Its vertex is not at the origin
What are characteristics of the graph of the linear parent function?
Please don't write "the following" if you don't provide a list.
What is the parent function for the exponential function?
The parent function of the exponential function is ax
Which parent function is represented by the graph?
Reciprocal parent function
What must be true about the coefficient of a linear function if that function experiences a vertical stretch of the parent function?
For a linear function to experience a vertical stretch of the parent function ( f(x) = mx + b ), the coefficient ( m ) (the slope) must be greater than 1. A vertical stretch means that the output values of the function are scaled up, making the graph steeper compared to the original. Thus, if the original function has a slope ( m ), the transformed function will have a slope of ( k \cdot m ) where ( k > 1 ).
Define parent function?
A parent function refers to the simplest function as regards sets of quadratic functions
What is the definition of parent function?
When a function is nested inside another function, the outer one is the parent, the inner is the child.
What is the parent function for a quadratic function?
y = x2 is the parent function, but it can be in the form y = ax2 + bx + c
Is a parent function a parabola?
A parent function is a basic function that serves as a foundation for a family of functions. The quadratic function, represented by ( f(x) = x^2 ), is indeed a parent function that produces a parabola when graphed. However, there are other parent functions as well, such as linear functions and cubic functions, which produce different shapes. Therefore, while the parabola is one type of parent function, it is not the only one.
What statements best describes the transformations of the function gx x 4 - 3 compared to its parent graph fx x?
If you want to ask questions about the "following", then I suggest that you make sure that there is something that is following.
