Question

Given the graph of a function f. A) Graph f(x) -3B) Graph f(x+4)C) Graph -f(x)See picture of the graph of function f attached

Answer 1

From the given problem, the figure shows the graph of f(x).

Note that translating the graph in a manner of :

`f(x)+c`

will shift the graph c units upward if the sign is positive or c units downward if the sign is negative.

We are looking for the graph of f(x) - 3

Since the sign is negative, we will shift the grahp 3 units downward, the graph will be like this.

As you can see, the orginal graph intersects at the origin (0, 0). The new graph intersects at (0, -3) since we moved or shifted the graph 3 units downward.

Additional :

If f(x) is translated in a manner of f(x+c), the graph will be shifted c units to the left if c is positive and will be shifted c units to the right if c is negative.

If f(x) is transformed in a manner of -f(x), the graph will reflect over the x-axis.

If the original point is (x, y). It will become (x, -y)