Suppose that a function f(x) is such that f(5)=10. a) find a point on the graph y=f(x). b) find a point on the graph of -3f(x-1)+4.

Answer 1

The fact that (5,10) is a point on the graph of f(x) means that when x = 5, y =10.

Suppose g(x) = -3f(x-1)+4.

Note that when x = 6:

g(6) = -3f(6-1)+4

g(6) = -3f(5) + 4

Since we know that f(5) = 10:

g(6) = -3(10) + 4 = -26

So a point on the graph of g is (6, -26).

Here is a graph containing 3 separate functions that satisfy the above criteria.

desmos.com/calculator/tuw21wisq0