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To apply the given transformations to the equation ( y = x^3 ), we start with the reflection across the x-axis, which gives us ( y = -x^3 ). Next, we apply the horizontal shift of 8 units to the left, resulting in ( y = - (x + 8)^3 ). Finally, we apply the vertical compression by a factor of ( \frac{1}{7} ), leading to the final equation: ( y = -\frac{1}{7}(x + 8)^3 ).
What else can I help you with?
What is the equation of a line with a slope of zero?
A horizontal line has a slope of zero. The equation of a horizontal line is y = a.
What is the equation of x squared plus y squared equals 16 with a horizontal compression of a half?
In order to take your circle and squash it horizontally to 1/2 of its original width (2),change the equation to4x2 + y2 = 16
What is equation of the horizontal line?
The equation of any horizontal line isY = a number .
What type of equation has a graph that is horizontal?
It is likely that a horizontal line on a graph will have the equation y=c, where c is a variable.
When is a linear equation an identity?
When the equation represents a horizontal line.
How do you find transformations in an equation?
To find transformations in an equation, you can look for changes in the coefficients and constants that affect the position, size, or shape of the graph. For example, a coefficient before the x term will affect the stretch or compression of the graph, while a constant added or subtracted will affect the vertical shift. Additionally, changes inside functions (such as squaring or square rooting) can also indicate transformations.
What is the equation of a line with a slope of zero?
A horizontal line has a slope of zero. The equation of a horizontal line is y = a.
What is the equation of x squared plus y squared equals 16 with a horizontal compression of a half?
In order to take your circle and squash it horizontally to 1/2 of its original width (2),change the equation to4x2 + y2 = 16
What is equation of the horizontal line?
The equation of any horizontal line isY = a number .
What type of equation has a graph that is horizontal?
It is likely that a horizontal line on a graph will have the equation y=c, where c is a variable.
When is a linear equation an identity?
When the equation represents a horizontal line.
What is the form of an equation for a horizontal line?
For a horizontal line, it is y= a value
What is an example of the equation of a horizontal line?
A horizontal line would be of the form y= (a number). There should be no 'x's involved in the equation.
Which transformations affect the slope of a linear function?
The slope of a linear function is affected by transformations that alter the function's coefficients or scaling. Specifically, vertical stretching or compressing changes the slope if the coefficient of the independent variable (x) is modified. Additionally, horizontal transformations, such as shifting the graph left or right, do not affect the slope but can change the intercept. Overall, any transformation that modifies the coefficient of x in the equation directly influences the slope.
How do you write equations for ertical and horizontal lines?
A vertical line has the equation [ x = a number ]. A horizontal line has the equation [ y = a number ].
What is a equation of a line?
The equation of any horizontal line isY = a number
When you shift the graph of an equation up or down does every instance of x in the equation change?
Yes, for example if you have y=x but you shifted the equation up 3 units hence: y=x+3. than you will receive a different y from every instance (point) of x. Reference: collegemathhelper.com/2015/11/horizontal-graph-transformations-for.html
