The function \( f \) is defined as follows. \( f(x)=\left\{\begin{array}{ll}-2 x+3 & \text { if } x<1 \\ 2 x-1 & \text { if } x \geq 1\end{array}\right. \) (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (a) The domain of the function \( f \) is \( (-\infty, \infty) \). (Type your answer in interval notation.) (b) Locate any intercepts. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no intercepts.

The domain of the function \( f \) is indeed all real numbers: \( (-\infty, \infty) \). This is because the function has rules for all \( x \), regardless of whether \( x \) is less than or greater than (or equal to) 1. For the intercepts: To find the **y-intercept**, set \( x = 0 \): \[ f(0) = -2(0) + 3 = 3. \] Thus, the y-intercept is \( (0, 3) \). To find the **x-intercept**, set \( f(x) = 0 \): 1. For \( x < 1 \): \[-2x + 3 = 0 \implies x = \frac{3}{2} \] (Not valid since \( x < 1 \) must hold). 2. For \( x \geq 1 \): \[2x - 1 = 0 \implies x = \frac{1}{2}. \] (Not valid since \( x \geq 1 \) must hold). Hence, the only intercept is the y-intercept at \( (0, 3) \). In conclusion, the correct choice is A. The intercept(s) is/are \( (0, 3) \).