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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 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 ).
What are the following functions state the vertex and what transformations on the parent function are needed to make the graph of the given function?
To determine the vertex and transformations of a given function, we first need the specific function itself. For example, if the function is in the form (f(x) = a(x-h)^2 + k), the vertex is ((h, k)). The transformations from the parent function (f(x) = x^2) would include a vertical stretch/compression by factor (a), a horizontal shift (h) units, and a vertical shift (k) units. If you provide the specific function, I can give a more detailed answer.
How does the graph of f(x) 3(4)x-5 plus 23 relate to its parent function?
The graph of the function ( f(x) = 3(4^x) - 5 + 23 ) is a transformation of its parent function ( g(x) = 4^x ). The factor of 3 vertically stretches the graph, making it steeper, while the "+23" shifts it upward by 23 units. The "-5" appears to be an error in your expression, as it would typically indicate a downward shift; if included, it would offset the upward shift. Overall, the graph retains the exponential growth characteristic of the parent function but is altered in scale and position.
What is the equation for cubic reflected over the x axis and vertical shift down 2?
A cubic function can be expressed in the form ( f(x) = ax^3 + bx^2 + cx + d ). To reflect this function over the x-axis, you negate it, resulting in ( f(x) = -ax^3 - bx^2 - cx - d ). To apply a vertical shift down by 2, you subtract 2 from the entire function, leading to the final equation: ( f(x) = -ax^3 - bx^2 - cx - (d + 2) ).
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 ).
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
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
What sources shift production function?
s shift in production function
What are the following functions state the vertex and what transformations on the parent function are needed to make the graph of the given function?
To determine the vertex and transformations of a given function, we first need the specific function itself. For example, if the function is in the form (f(x) = a(x-h)^2 + k), the vertex is ((h, k)). The transformations from the parent function (f(x) = x^2) would include a vertical stretch/compression by factor (a), a horizontal shift (h) units, and a vertical shift (k) units. If you provide the specific function, I can give a more detailed answer.
How does the graph of f(x) 3(4)x-5 plus 23 relate to its parent function?
The graph of the function ( f(x) = 3(4^x) - 5 + 23 ) is a transformation of its parent function ( g(x) = 4^x ). The factor of 3 vertically stretches the graph, making it steeper, while the "+23" shifts it upward by 23 units. The "-5" appears to be an error in your expression, as it would typically indicate a downward shift; if included, it would offset the upward shift. Overall, the graph retains the exponential growth characteristic of the parent function but is altered in scale and position.
The keyboard shortcut for the Insert Function is?
[shift] + [F3]
What is the equation for cubic reflected over the x axis and vertical shift down 2?
A cubic function can be expressed in the form ( f(x) = ax^3 + bx^2 + cx + d ). To reflect this function over the x-axis, you negate it, resulting in ( f(x) = -ax^3 - bx^2 - cx - d ). To apply a vertical shift down by 2, you subtract 2 from the entire function, leading to the final equation: ( f(x) = -ax^3 - bx^2 - cx - (d + 2) ).
