Question

What does g(3⋅t+3) do to the function g(t) ?

shift 3 units left and then compress horizontally by a factor of 1/3

compress horizontally by a factor of 1/3 and then shift left 3 units

compress horizontally by a factor of 1/3then shift 3 units left

shift 3 units left and then compress horizontally by a factor of 1/3

Answer 1

Given a function f(x), a new function g(x)=f(bx), where b is a constant, is a horizontal stretch or horizontal compression of the function f(x), where if b>1, then the graph will be compressed by 1/b.

Given a function f(x), a new function g(x)=f(x−h), where h is a constant, is a horizontal shift of the function f. If h is positive, the graph will shift right. If h is negative, the graph will shift left.

From the above discussion, the graph is first compressed by a factor of 1/3 and the shifted left 3 units.