Explanation:
f(x) = x^2 represents a quadratic function, where the input value (x) is squared and the resulting output value is equal to the square of x.
g(x) = (x+3)^2 - 1 represents another quadratic function, where the input value (x) is first added to 3, then squared, and the resulting output value is equal to the square of (x+3) minus 1.
To evaluate these functions for a specific value of x, we simply substitute that value into the function in place of x. For example, if we want to find f(4), we would replace x with 4 to get:
f(4) = 4^2 = 16
Similarly, if we want to find g(-2), we would replace x with -2 to get:
g(-2) = (-2+3)^2 - 1 = 1^2 - 1 = 0
We can also graph these functions on a coordinate plane by plotting points for various values of x and their corresponding values of f(x) or g(x). The graph of f(x) = x^2 is a parabola that opens upwards, while the graph of g(x) = (x+3)^2 - 1 is also a parabola, but it has been shifted 3 units to the left and 1 unit downwards compared to the graph of f(x).