The transformation form for g(x) is: y = ±A(x) + D
where: A is the slope of the graph , D is the y-intercept of the graph .
The transformation(s) of f(x) needed to create g(x) are:
Horizontal reflection
Vertical dilation by a factor of 2
Translation 2 units to the right
To reflect the graph of f(x) across the y-axis, we multiply by -1:
f(x) = x
g(x) = -1 * f(x)
To vertically dilate the graph of f(x) by a factor of 2, we multiply by 2:
g(x) = -1 * 2 * f(x)
To translate the graph of g(x) 2 units to the right, we add 2:
g(x) = -1 * 2 * f(x) + 2
Therefore, the equation of g(x) is:
g(x) = -2x + 2
We can also see this transformation from the graph.
The graph of g(x) is a reflection of the graph of f(x) across the y-axis, stretched vertically by a factor of 2, and moved 2 units to the right.
Edit the Transforming Function
To edit the transforming function, we can simply enter the equation of g(x) into the text box.
The text box will automatically update the graph to match the equation.
Transforming Function: -2x + 2
Transformation Form
The transformation form for g(x) is:
y = ±A(x) + D
where:
A is the slope of the graph
D is the y-intercept of the graph
In this case, A = -2 and D = 2.