Answer:
A transformation of a function is a change in its graph, such as shifting, stretching, compressing, or reflecting it. There are some rules to determine how a transformation affects the graph of a function.
Explanation:
If you add or subtract a constant to the input of the function (x), you shift the graph horizontally by that constant. For example, f(x+1) shifts the graph of f(x) one unit to the left.
If you add or subtract a constant to the output of the function (y), you shift the graph vertically by that constant. For example, f(x)+2 shifts the graph of f(x) two units up.
If you multiply or divide the input of the function by a constant, you stretch or compress the graph horizontally by that constant. For example, f(2x) compresses the graph of f(x) by a factor of 2.
If you multiply or divide the output of the function by a constant, you stretch or compress the graph vertically by that constant. For example, 2f(x) stretches the graph of f(x) by a factor of 2.
If you negate the input or the output of the function, you reflect the graph over the x-axis or y-axis. For example, -f(x) reflects the graph of f(x) over the x-axis.
In your case, g(x) = f(x+1) means that you are adding 1 to the input of f(x). This means that you are shifting the graph of f(x) one unit to the left. The shape and size of the graph remain unchanged.