Given the following functions f(x) and g(x), describe the changes (horizontal shifts, vertical shifts, etc.) to the graph of g(x) with respect to the graph of f(x). * 3 points
f(x)=lxl g(x)= -lx+3l-2
i spelt my name wrong lol
f(x) = |x| is a big "V" with the vertex at the origin
adding 3 to x shifts the "V" 3 units to the left
the leading minus sign inverts the "V"
the minus 2 shifts the graph 2 units down
To describe the changes between the graphs of f(x) and g(x), we can compare their equations and identify any differences.
1. Vertical Shift:
- The equation of f(x) is lxl, which is the absolute value of x. This function has no vertical shift since there is no term added or subtracted.
- The equation of g(x) is -lx+3l-2. Here, the absolute value part (-lx+3l) implies a vertical shift of 3 units downwards, as compared to f(x). The constant term -2 represents a vertical shift of 2 units further downwards.
2. Horizontal Shift:
- The equation of f(x) = lxl does not involve any horizontal shift. The graph of f(x) is symmetric with respect to the y-axis.
- The equation of g(x) = -lx+3l-2 contains the term -x. This term indicates a horizontal shift of the graph to the right by 3 units when compared to f(x).
The sign before x (-x) inverses the direction of the shift.
Therefore, the changes in the graph of g(x) compared to f(x) are:
- A vertical shift of 3 units downwards.
- A vertical shift of an additional 2 units downwards.
- A horizontal shift of 3 units to the right.