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
The parent function, f left-parenthesis x right-parenthesis equals log x, is used to graph g left-parenthesis x right-parenthesis equals 3 log left-parenthesis negative x plus 2 right-parenthesis minus 6. Which transformation should be applied first?
The transformation that should be applied first is a horizontal reflection.
In the parent function f(x) = log(x), the log function is reflected over the y-axis compared to the parent function y = x.
Therefore, to obtain the graph of g(x) = 3 log(-x + 2) - 6, the first transformation to be applied should be the horizontal reflection over the y-axis.
options
vertical stretch by a factor of 3
reflection over the y-axis
horizontal shift left 2 units
vertical shift down 6 units
The correct option for the transformation that should be applied first is:
reflection over the y-axis.
wrong
Apologies for the confusion. The correct option for the transformation that should be applied first is:
horizontal shift left 2 units.
The graph of g left-parenthesis x right-parenthesis is a transformation of its parent function, f left-parenthesis x right-parenthesis equals Start Root x End Root. Which function defines g left-parenthesis x right-parenthesis
To determine the function that defines g(x), we need more information about the specific transformation applied to the parent function f(x) = √x. Please provide the information regarding the transformation or any additional given details.
options
g left-parenthesis x right-parenthesis equals 2 Start Root x End Root plus 4Image with alt text: g left-parenthesis x right-parenthesis equals 2 Start Root x End Root plus 4
g left-parenthesis x right-parenthesis equals Start Root 2 left-parenthesis x plus 4 right-parenthesis End Root
Image with alt text: g left-parenthesis x right-parenthesis equals Start Root 2 left-parenthesis x plus 4 right-parenthesis End Root
g left-parenthesis x right-parenthesis equals Start Root x minus 4 End Root plus 2
Image with alt text: g left-parenthesis x right-parenthesis equals Start Root x minus 4 End Root plus 2
g left-parenthesis x right-parenthesis equals 2 Start Root x minus 4 End Root
The correct function that defines g(x) is:
g(x) = Start Root x minus 4 End Root plus 2
that is wrong
Apologies for the previous incorrect response. Please provide the correct function options again, and I will be happy to assist you in determining the function that defines g(x).
g left-parenthesis x right-parenthesis equals 2 Start Root x End Root plus 4Image with alt text: g left-parenthesis x right-parenthesis equals 2 Start Root x End Root plus 4
g left-parenthesis x right-parenthesis equals Start Root 2 left-parenthesis x plus 4 right-parenthesis End Root
Image with alt text: g left-parenthesis x right-parenthesis equals Start Root 2 left-parenthesis x plus 4 right-parenthesis End Root
g left-parenthesis x right-parenthesis equals Start Root x minus 4 End Root plus 2
Image with alt text: g left-parenthesis x right-parenthesis equals Start Root x minus 4 End Root plus 2
g left-parenthesis x right-parenthesis equals 2 Start Root x minus 4 End Root
Apologies for the previous misunderstanding. The correct function that defines g(x) is:
g(x) = 2√(x - 4)