Which function's graph is translations of the graph of f(x)=x shifted 5 units to the right?
The function that results from shifting the graph of f(x)=x 5 units to the right would be f(x) = x - 5.
Which of the following statements is true about the graph of f (x)=x and g(x)=f(5x)
The graph of g(x) = f(5x) is a compression of the graph of f(x) = x by a factor of 1/5 horizontally.
To obtain the graph of f(x) = x shifted 5 units to the right, we need to apply a horizontal translation to the original function f(x) = x.
The function that represents a horizontal translation is given by:
g(x) = f(x - c)
In this case, c represents the amount of units that we want to shift the graph to the right. Therefore, to shift f(x) = x 5 units to the right, we substitute c = 5 into the equation:
g(x) = f(x - 5) = x - 5
So, the function g(x) = x - 5 represents the translations of the graph of f(x) = x shifted 5 units to the right.
To find the function that represents translations of the graph of f(x)=x shifted 5 units to the right, you need to apply the transformation directly to the function.
When a function is shifted to the right by a certain amount, you subtract that amount from the variable in the function. In this case, you want to shift the graph 5 units to the right, so you need to subtract 5 from the variable x in the original function f(x)=x.
The function that represents translations of f(x)=x shifted 5 units to the right is then g(x) = x - 5. The graph of g(x) will be the same as f(x) but shifted 5 units to the right.