suppose that g(x) = f(x)+ which statement best compares the graph of g(x) with the graph of f(x)
we conclude that g(x) = f(x – 2) + 3 means the graph of g(x) is shifted 2 units right and 3 units up.
Step-by-step explanation:
To shift a function right
Subtract inside the function's argument. For example, is basically shifted b units to the right.
Subtracting inside the function's argument moves you to the right.
So, g(x) = f(x – 2) means f(x) is shifted two units to the right.
and to move a function up
Add outside the function. For example, is basically moved up units.
So, g(x) = f(x – 2) + 3 means, f(x) is moved 3 units up.
Therefore, overall, after two transformations, we conclude
that g(x) = f(x – 2) + 3 means the graph of g(x) is shifted 2 units right and 3 units up.
Answer is............
--------->The graph of g(x) is shifted 2 units right and 3 units up.<---------
To compare the graph of g(x) with the graph of f(x), let's consider the statement "g(x) = f(x)+".
The "+" symbol in the equation indicates that g(x) is obtained by shifting the graph of f(x) upwards by a certain amount. Specifically, the graph of f(x) is shifted vertically upward by the value represented by the "+" symbol.
In other words, the graph of g(x) will be the same as the graph of f(x) but shifted upwards vertically.
Therefore, the statement "g(x) = f(x)+" means that the graph of g(x) is obtained by shifting the graph of f(x) upwards.
To compare the graphs of g(x) and f(x), we first need to understand what the statement "g(x) = f(x)+" means.
In this statement, the "+" sign is used to represent some additional function or term that is added to f(x) to obtain g(x). This means that g(x) is obtained by taking the values of f(x) and then adding some extra values or altering the graph in some way.
To compare the graphs of g(x) and f(x), we can consider a few scenarios:
1. If the additional function or term added to f(x) is positive for all values of x, then g(x) will be greater than or equal to f(x) at every point. In this case, the graph of g(x) will be at or above the graph of f(x).
2. If the additional function or term added to f(x) is negative for all values of x, then g(x) will be less than or equal to f(x) at every point. In this case, the graph of g(x) will be at or below the graph of f(x).
3. If the additional function or term added to f(x) varies for different values of x, then g(x) may lie above or below f(x) depending on the values of x. The graph of g(x) may cross or intersect the graph of f(x) at certain points.
Based on this analysis, the best statement to compare the graphs of g(x) and f(x) would depend on the nature of the additional function or term added to f(x) in the equation g(x) = f(x)+.