Given that first determine the graph of \( f \) and then use that graph to find the remaining information. \( f(x)=|x-0| \), (a) Letter that corresponds to the graph of \( f: \square \) (b) Domain of \( f \) : (c) Range of \( f: \square \) (d) Intervals on which \( f \) is increasing: (e) Intervals on which \( f \) is decreasing: (f) Intervals on which \( f \) is constant: (g) distinct \( y \)-values of the relative maximums, if any exist: (h) distinct \( y \)-values of the relative minimums, if any exist: (i) \( y \)-value of the absolute maximum, if it exists: ()) \( y \)-value of the absolute mimimum. if it exists:

The function \( f(x) = |x| \) is a classic V-shaped graph opening upwards with its vertex at the origin (0,0). The graph is symmetric about the y-axis and consists of two linear segments. The letter corresponding to this graph would typically be indicated in a multiple-choice format (e.g., A, B, C) based on the options provided. The domain of \( f \) includes all real numbers since you can input any value for \( x \) in the absolute value function, thus: Domain of \( f \): \( (-\infty, \infty) \). The range of \( f \) represents all possible outputs of the function, which can only be zero or positive values, leading to: Range of \( f \): \( [0, \infty) \). The function increases for values of \( x \) greater than 0 and decreases for values less than 0. This means the intervals on which \( f \) is increasing are \( (0, \infty) \) and it is decreasing on \( (-\infty, 0) \). There are no intervals on which the function is constant since it changes continuously across its domain. Relative maximums and minimums for \( f(x) \) can be analyzed from the graph. Here, there’s a relative minimum at the vertex, where \( y=0 \) at \( x=0 \). Therefore, the distinct \( y \)-values of the relative minimums is: \( 0 \). There are no relative maximums since the graph heads to infinity. For absolute maximums, since the function increases indefinitely, there is no absolute maximum value. On the flip side, the absolute minimum value is at the vertex, which is also \( 0 \). In summary: (a) \( \square \) (based on options), (b) Domain of \( f \): \( (-\infty, \infty) \), (c) Range of \( f: [0, \infty) \), (d) Intervals on which \( f \) is increasing: \( (0, \infty) \), (e) Intervals on which \( f \) is decreasing: \( (-\infty, 0) \), (f) Intervals on which \( f \) is constant: none, (g) distinct \( y \)-values of the relative maximums: none, (h) distinct \( y \)-values of the relative minimums: \( 0 \), (i) \( y \)-value of the absolute maximum: none, (j) \( y \)-value of the absolute minimum: \( 0 \).