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If you vertically shift the linear parent function F(x) x down six units what is the equation of the new function?
To vertically shift the linear parent function ( F(x) = x ) down six units, you subtract 6 from the function. The new equation becomes ( F(x) = x - 6 ). This transformation moves the entire graph downward by 6 units while maintaining its linear characteristics.
If you apply the changes below to the linear parent function f(x) x what is the equation of the new function?
To determine the equation of the new function after applying changes to the linear parent function ( f(x) = x ), we need to know the specific transformations applied, such as shifts, stretches, or reflections. For example, if we apply a vertical shift up by 3 units, the new function would be ( f(x) = x + 3 ). If we apply a horizontal shift to the right by 2 units, it would be ( f(x) = x - 2 ). Please provide the specific changes for a precise new equation.
If you apply the changes below to the absolute value parent function F(x) x what is the equation of the new function Shift 8 units left. Shift 3 units Dow?
To shift the absolute value parent function ( F(x) = |x| ) eight units to the left, you replace ( x ) with ( x + 8 ), resulting in ( F(x) = |x + 8| ). Then, to shift the function down three units, you subtract 3 from the entire function, yielding the final equation ( F(x) = |x + 8| - 3 ).
If you horizontally shift the absolute value parent function F(x) x left three units what is the equation of the new function?
To horizontally shift the absolute value parent function ( F(x) = |x| ) three units to the left, you replace ( x ) with ( x + 3 ). This results in the new function ( F(x) = |x + 3| ). Thus, the equation of the shifted function is ( F(x) = |x + 3| ).
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).
If you vertically shift the linear parent function F(x) x down six units what is the equation of the new function?
To vertically shift the linear parent function ( F(x) = x ) down six units, you subtract 6 from the function. The new equation becomes ( F(x) = x - 6 ). This transformation moves the entire graph downward by 6 units while maintaining its linear characteristics.
If you apply the changes below to the linear parent function f(x) x what is the equation of the new function?
To determine the equation of the new function after applying changes to the linear parent function ( f(x) = x ), we need to know the specific transformations applied, such as shifts, stretches, or reflections. For example, if we apply a vertical shift up by 3 units, the new function would be ( f(x) = x + 3 ). If we apply a horizontal shift to the right by 2 units, it would be ( f(x) = x - 2 ). Please provide the specific changes for a precise new equation.
If you vertically shift the linear parent function F(x) x up 2 units then horizontally compress it by multiplying by 7 what is the equation of the new function G(x)?
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If you apply the changes below to the absolute value parent function F(x) x what is the equation of the new function Shift 8 units left. Shift 3 units Dow?
To shift the absolute value parent function ( F(x) = |x| ) eight units to the left, you replace ( x ) with ( x + 8 ), resulting in ( F(x) = |x + 8| ). Then, to shift the function down three units, you subtract 3 from the entire function, yielding the final equation ( F(x) = |x + 8| - 3 ).
If you horizontally shift the absolute value parent function F(x) x left three units what is the equation of the new function?
To horizontally shift the absolute value parent function ( F(x) = |x| ) three units to the left, you replace ( x ) with ( x + 3 ). This results in the new function ( F(x) = |x + 3| ). Thus, the equation of the shifted function is ( F(x) = |x + 3| ).
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).
To shift the graph of an equation a certain number of units up you need to that number to from the function's equation?
Add
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.
If you shift the quadratic parent function f(x) x2 left 12 units what is the equation of the new function?
f(x) = (x + 12)2
How can transformations alter the graph of a parent function?
OK, so let's call the parent function you're given f(x). There's a series of transformations a parent function can go through:-f(x) = makes the parent function reflect over the x-axisOn the other hand, f(-x) = makes it reflect over the y-axisf(x+a) = makes the parent function shift a units to the leftf(x-a) = makes the parent function shift a units to the rightf(x)+a = makes the parent function shift a units upf(x)-a = makes the parent function shift a units downf(ax) if x is a fraction like 1/2 , makes the parent function stretch by a factor of 2 (or multiply each x by 2)f(ax) if x is a whole number (or fractions greater or equal to 1) like 2, makes the parent function compress by a factor of 2 (or divide each x by 2)a*f(x) if x is a fraction like 1/2, makes the parent function get shorter by a factor of 2 (or divide each y by 2)a*f(x) if x is a whole number (or fractions greater or equal to 1) like 2, makes the parent function get taller by a factor of 2 (or multiply each y by 2)One way you can always tell what to do is that everything that is INSIDE the parentheses will be the OPPOSITE of what you think it should do. OUTSIDE the parentheses will do EXACTLY what you think it should do.And when performing the transformations, start inside the parentheses first and then move outside. For example, f(x-2)+2; move the parent function first to the right 2 units and THEN move it up 2 units.
How does changing the constant affect a graph?
Changing the constant in a function will shift the graph vertically but will not change the shape of the graph. For example, in a linear function, changing the constant term will only move the line up or down. In a quadratic function, changing the constant term will shift the parabola up or down.
Write an equation of the cosine function with amplitude two thirds period 1.8 phase shift -5.2 and vertical shift 3.9?
y=2/3cos(1.8b-5.2)+3.9
