The function \( f \) is defined as follows. \( f(x)=\left\{\begin{array}{ll}2 x & \text { if } x \neq 0 \\ 3 & \text { if } x=0\end{array}\right. \) (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 (Type your answer in interval notation.)

The domain of the function \( f \) is all real numbers since it is defined for every value of \( x \) (both when \( x \neq 0 \) and at \( x = 0 \)). In interval notation, this is expressed as \( (-\infty, \infty) \). Now, let's delve into the intercepts! For the y-intercept, set \( x = 0 \): \( f(0) = 3 \). For the x-intercept, set \( f(x) = 0 \); since \( f(x) = 2x \) when \( x \neq 0 \), \( 2x = 0 \) gives \( x = 0 \). Thus, the function has x-intercept only at the point \( (0, 3) \). Graphing refers to visually portraying these values, where you likely see a straight line for \( f(x) = 2x \) and a distinct point at \( (0,3) \). The range splits based on graphing: all y-values from 0 up, but excluding the segment for \( f(0) \).