Graph the function - Precalc

Question

Graph the function by starting with at least three points of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting to find the points of the function given.

f(x) = - (x + 7)² - 7

Answer 1

By using function transformation rules, you can write: the parent function x² will be transformed as shift to left by 7 units, symmetric reflection related to horizontal axes, and translate dawn by 7 units.

Now, you can easy graph the given function.

Answer 2

The "basic function" is f(x) = x²

The transformations you go through to get to f(x) = -(x + 7)² - 7 are these:

1. Subtract 7 from the "x"
2. Take a negative of the "y"
3. Subtract 7 from the y obtained above

So a table of values showing the basic function x's (x_b) and y's (y_b) is as follows:

Notice that to each x_b I subtract 7 to get to the "x" and to each y_b, I switch the sign, then subtract 7.

Then you can graph the function using (x, f(x)) points.