Question

does the function have a minimum x - value?
yes no
does the function have a maximum x - value?
yes no
select a statement to describe the domain:
does the function have a minimum y - value?
yes no
(graph with a coordinate plane, a vertical line at x = 0, a point at (0,25), and a green point at (1,5) (approximate) with lines forming a graph)

Explanation:

Step1: Analyze minimum x - value

The graph's x - axis has a green dot at \(x = 5\) (from the grid, the green dot is at \(x = 5,y = 1\) approximately? Wait, looking at the x - axis, the green dot is at \(x=5\) (since the x - grid lines are at 0,5,10,15...). The function's x - values start from \(x = 5\)? Wait, no, the vertical line is at \(x = 0\) (the y - axis) and the green dot is at \(x = 5\). Wait, the domain of x: the leftmost point of the function (the green dot) is at \(x = 5\)? Wait, no, the graph has a green dot at \(x = 5\) (horizontal position) and then lines. Wait, for minimum x - value: the function's x - values start at \(x = 5\)? Wait, no, looking at the graph, the green dot is at \(x = 5\) (x - coordinate 5), and the other parts: the vertical line is at \(x = 0\) (y - axis), but the function (the lines) start at \(x = 5\)? Wait, no, the green dot is at \(x = 5\), so the minimum x - value of the function (the part with the lines) is \(x = 5\)? Wait, the question is "Does the function have a minimum x - value?". Since the function (the line segments) have a left - most point at \(x = 5\) (the green dot), so there is a minimum x - value (the smallest x - value the function takes is 5). Wait, but the options are Yes or No. Wait, maybe I misread. Wait, the vertical line is at \(x = 0\) (y - axis), but the function (the non - vertical part) starts at \(x = 5\). So the function's x - values start at \(x = 5\), so the minimum x - value is 5, so the answer for "Does the function have a minimum x - value?" is Yes? Wait, no, maybe the vertical line is part of the function? Wait, the vertical line is at \(x = 0\), from \(y=-5\) to \(y = 5\)? But the green dot is at \(x = 5,y = 1\), and the other line goes to \((25,0)\) and beyond? Wait, maybe I made a mistake. Wait, let's re - examine: the graph has a vertical line at \(x = 0\) (y - axis) and a green dot at \(x = 5\). The function (the lines) have x - values starting at \(x = 5\), so the minimum x - value of the function (the line part) is 5, so there is a minimum x - value (the smallest x the function attains is 5), so answer Yes? Wait, but maybe the vertical line is not part of the function. Wait, the problem is about the function shown. Let's check the other parts.

Step2: Analyze maximum x - value

The graph has lines going to the right, so the x - values can go to infinity? So there is no maximum x - value, so answer No.

Step3: Analyze minimum y - value

The y - axis: the green dot is at \(y = 1\), and the other line goes to \(y = 0\) at \(x = 25\), and the vertical line goes from \(y=-5\) to \(y = 5\). Wait, is the vertical line part of the function? If the vertical line is part of the function, then the minimum y - value is \(-5\). But if the vertical line is not part of the function (only the line segments with the green dot and the other points), then the minimum y - value: the green dot is at \(y = 1\), and the line to \((25,0)\) has \(y\) going down to 0, and the other line goes up? Wait, no, the graph has a green dot at \(x = 5,y = 1\), a point at \((25,0)\), and another line going up. Wait, maybe the function is a piece - wise function. But for minimum y - value: if the vertical line is part of the function, then \(y\) can go down to \(-5\), so there is a minimum y - value. But maybe the vertical line is the y - axis, not part of the function. Wait, the problem's graph: the vertical line is the y - axis (x = 0), and the function (the lines) start at \(x = 5\). So the function (the line segments) have y - values: the green dot is at \(y = 1\), the point at \((25,0)\) (y = 0), and the other line goes up. So the minimum y - value of the function (the line part) is 0? Wait, no, the point at \((25,0)\) has \(y = 0\), and the green dot has \(y = 1\), so the minimum y - value is 0, so there is a minimum y - value? Wait, but the options are Yes or No.

Wait, maybe I should re - look at the graph. The green dot is at \(x = 5,y = 1\) (assuming the grid: x - axis labels 0,5,10,... and y - axis labels - 5, - 4,...0,1,2...). The line from the green dot to \((25,0)\) has a slope, so as x increases from 5 to 25, y decreases from 1 to 0. Then another line from \((25,0)\) going up. So the minimum y - value of the function (the line part) is 0, so there is a minimum y - value (Yes). But maybe the vertical line (x = 0) is not part of the function.

But let's answer the first question: "Does the function have a minimum x - value?". The function (the line segments) have a left - most point at \(x = 5\) (the green dot), so the smallest x - value the function takes is 5, so there is a minimum x - value, so answer Yes.

"Does the function have a maximum x - value?": The lines go to the right (the line from \((25,0)\) goes to the right, x increasing), so x can go to infinity, so no maximum x - value, answer No.

"Does the function have a minimum y - value?": The function (the line part) has a minimum y - value of 0 (at \(x = 25\)), so yes, answer Yes. But maybe I made a mistake. Wait, the green dot is at \(x = 5,y = 1\), the point at \((25,0)\) (y = 0), and the other line goes up. So the minimum y is 0, so yes.

But let's focus on one question, say "Does the function have a minimum x - value?".

Answer:

For "Does the function have a minimum x - value?": Yes
For "Does the function have a maximum x - value?": No
For "Does the function have a minimum y - value?": Yes