Question

write the function f(x) that represents the described transformation. reflect over x-axisstretch by a factor of 6right 1 down 2

Answer 1

The function f(x) after the transformations would be:

`-6f(x-1)-2`

This comes from the following facts:

Suppose c>0. to obtain the graph of:

• f(x)+c, shift the graph of f(x) c units upward.

,

• f(x)-c, shift the graph of f(x) c units downward.

,

• f(x-c), shift the graph of f(x) c units to the right.

,

• f(x+c), shift the graph of f(x) c units to the left.

Suppose c>1. to obtain the graph of:

cf(x), stretch the graph of f(x) by a factor of c.

(1/c)f(x), shrink the graph of f(x) by a factor of c.

f(x/c), stretch the graph horizontally of f(x) by a factor of c.

f(cx), shrink the graph horizontally of f(x) by a factor of c.

-f(x)