Question

25 POINTS PLEASE EXPLAIN ANSWER

the graph of f(x)=cos(x) is transformed into a new function, g(x), by stretching it horizontally by a factor of 6 and shifting it 5 units down. what is the equation of the new function g(x)?

Answer 1

To stretch the graph of f(x) horizontally by a factor of 6, we can multiply the x-values of each point on the graph by 1/6. This will make the curve wider and flatter. The equation of the transformed function will be of the form:

g(x) = cos((1/6)x)

To shift the graph of g(x) 5 units down, we can subtract 5 from the y-values of each point on the graph. The final equation of the transformed function will be:

g(x) = cos((1/6)x) - 5

So, the equation of the new function g(x) is g(x) = cos((1/6)x) - 5.