The graphs of linear functions f and g are shown on the grid.
Which function is best represented by the graph of g?
The graphs of linear functions f and g are shown on the grid.
Which function is best represented by the graph of g?
g(x)=f(x)+2
g(x)=f(x)-2
g(x)=-f(x)-2
g(x)=-f(x)+2
Unfortunately, I'm unable to directly see the graphs you are referencing as I'm just a text-based assistant. However, I can help you determine which function would represent `g` based on its relation to `f`.
If the graph of function g is a vertical shift of the graph of function f, then the relationship between f and g will be as follows:
- If g is shifted upwards by 2 units from f on the graph, then the equation of g will be `g(x) = f(x) + 2`.
- If g is shifted downwards by 2 units from f on the graph, then the equation of g will be `g(x) = f(x) - 2`.
- If g is a reflection of f across the x-axis and then shifted downwards by 2 units, the equation of g will be `g(x) = -f(x) - 2`.
- If g is a reflection of f across the x-axis and then shifted upwards by 2 units, the equation of g will be `g(x) = -f(x) + 2`.
In order to determine which equation best represents the graph of `g`, you'll need to compare the position of the graph of `g` relative to `f`:
- If the graph is shifted upwards without being reflected, choose `g(x) = f(x) + 2`.
- If the graph is shifted downwards without being reflected, choose `g(x) = f(x) - 2`.
- If the graph is reflected across the x-axis and then shifted downwards, choose `g(x) = -f(x) - 2`.
- If the graph is reflected across the x-axis and then shifted upwards, choose `g(x) = -f(x) + 2`.
Carefully examine the position and orientation of the graphs of f and g on the grid to make your selection. Remember, a reflection across the x-axis will change the slope from positive to negative or vice versa, and a vertical shift will move the entire graph up or down without changing the slope.