Question

Question 1, 13.7 .7 Part 1 of 2 Determine the value of h in the translation. Describe the phase shift (use a phrase like " 3 units to the left" ) g(t)=f(t+7) Determine the value of h in the translation. h

Answer 1

The value of h in the expression g(t)=f(t+7) is 7, representing a phase shift or a horizontal shift of the function f(t) by 7 units to the left.

Step-by-step explanation:

In the function g(t)=f(t+7), the value of h (which represents a horizontal shift in the context of translations of functions) is 7. This indicates a horizontal shift in the function f(t) to the left. When considering periodic functions such as sine and cosine, this shift corresponds to a phase shift. In terms of a phase shift description, g(t) is the result of shifting f(t) 7 units to the left.

The concept of phase shift often comes up in trigonometric functions when modeling oscillatory motions, such as a block on a spring in Simple Harmonic Motion (SHM). In this context, a cosine function may be represented as x(t) = A cos(ωt + φ), where φ is the phase shift. If φ is positive, the function shifts to the left; if φ is negative, the function shifts to the right.