QuestionQuestion 1 (2 points) Given the following sine function, $$f(x)=2 \sin (\pi x)+1$$ determine the information below. Enter your answers as integers (no decimals are needed).
Amplitude $=$ $\square$ A
Midline at $\mathrm{y}=$ $\square$ A
Period $=$ $\qquad$ A $y$-intercept (enter a coordinate point with brackets and no spaces): $\square$ A
Domain (enter an interval): $\square$ A
Range (enter an interval): $\square$

Studdy Solution
The range of the function is determined by the amplitude and the midline. The sine function oscillates between $-1$ and $1$, so:
$$\text{Minimum value} = 1 - 2 = -1$$ $$\text{Maximum value} = 1 + 2 = 3$$
Range $= [-1, 3]$
The answers are: - Amplitude $= 2$ - Midline at $y = 1$ - Period $= 2$ - Y-intercept $= (0, 1)$ - Domain $= (-\infty, \infty)$ - Range $= [-1, 3]$