dentify the transformations used to graph g left-parenthesis x right-parenthesis equals negative one-half left-parenthesis x minus 3 right-parenthesis cubed from its parent function, f left-parenthesis x right-parenthesis equals x cubed.
To determine the transformations used to graph g(x) = -1/2(x - 3)^3 from its parent function f(x) = x^3, we need to look at three main transformations:
1. Horizontal translation: The function g(x) is translated to the right by 3 units compared to f(x). This is represented by the term (x - 3) in g(x).
2. Vertical reflection: The function g(x) is reflected vertically compared to f(x) due to the coefficient -1/2 in front of (x - 3)^3. This reflects the function vertically about the x-axis.
3. Stretching or compression: The function g(x) is compressed vertically compared to f(x) due to the coefficient -1/2 multiplying the entire function. This compresses the function by a factor of 2 in the y-direction.
Therefore, the transformations applied to f(x) to obtain g(x) are a translation to the right by 3 units, a vertical reflection about the x-axis, and a vertical compression by a factor of 2.
identify the transformations used to graph g left-parenthesis x right-parenthesis equals negative one-half left-parenthesis x minus 3 right-parenthesis cubed from its parent function, f left-parenthesis x right-parenthesis equals x cubed.
To graph g(x) = -1/2(x - 3)^3 from its parent function f(x) = x^3, we can identify the following transformations:
1. Horizontal translation: The function g(x) is shifted to the right by 3 units compared to f(x). This is represented by the expression (x - 3) in g(x).
2. Vertical reflection: The function g(x) is reflected vertically about the x-axis compared to f(x). The negative sign in front of 1/2 reflects the function vertically.
3. Vertical compression: The function g(x) is vertically compressed compared to f(x) with a scale factor of 1/2. This is determined by the coefficient -1/2 multiplying the entire function.
To summarize, the transformations applied to f(x) to obtain g(x) are a translation to the right by 3 units, a vertical reflection, and a vertical compression by a factor of 1/2.
options
a) a vertical shift down 3 units, a reflection over the y-axis, and a vertical stretch by a factor of 2
b) a horizontal shift right 3 units, a reflection over the x-axis, and a vertical compression by a factor of 2
c) a horizontal shift left 3 units, a reflection over the x-axis, and a horizontal compression by a factor of 2
d) a horizontal shift right 3 units, a reflection over the y-axis, and a horizontal stretch by a factor of one-half
The correct option is:
d) a horizontal shift right 3 units, a reflection over the y-axis, and a horizontal stretch by a factor of one-half
wrong
I apologize for the incorrect response. The correct option should be:
b) a horizontal shift right 3 units, a reflection over the x-axis, and a vertical compression by a factor of 2.
Which transformation should be applied last?
options
a) vertical stretch by a factor of 3
b) reflection over the y-axis
c) horizontal shift left 2 units
d) vertical shift down 6 units
The correct option for the transformation that should be applied last is:
d) vertical shift down 6 units