disciminant

A is the stretcher, because when you multiply the y coordinate by A, it gets A times further from the x axis. The points further from the axis get moved further than the points closer to the axis.

c is added to the y coordinate, so it shifts every point by the same amount.

Subtracting h from the x values requires that the x values be h units greater in order to get the same y values. So subtracting h from your x values shifts the graph to the right.

Here's a summary of what you should know about shifting and stretching, and the basic functions, at this point:

There are four types of basic functions at this point, the linear function y = x, the exponential function y = 2^x, the quadratic function y = x^2 and the power functions y = x^p (for any fixed value of p).

You should be able quickly, without a calculator, to evaluate these functions at x = -3, -2, -1, 0, 1, 2, 3 and graph them, and you should thereby understand the basic shapes of these graphs.

You should also be able to similarly evaluate the power functions at x = 1/2 and use this point in the graphing of your power function.

You should understand what points are designated as the 'basic points' of each function (x = 0 and x = 1 point for linear, x = -1, x = 0 and x = 1 points for quadratic, x = 0 and x = 1 points for exponential along with the understanding that the negative x axis is a horizontal asymptote, x = -1, x = 0, x = 1/2, x = 1 and x = 2 points for a power function).

You should be able to make a reasonable graph of each basic function given from only its basic points.

You should understand that y = A f(x - h) + c stretches every point of the y = f(x) graph A times as far from the x axis, shifts every point h units in the x direction, and shifts every point c units in the y direction.

Specifically you should be able to apply these transformations to the basic points and sketch the resulting graph based on only these points and your knowledge of the shape and general behavior of the function.