Question

identify each characteristic for the graph of the function shown.
select the number of y-intercepts: 1
enter the coordinates of the y-intercept:
select the number of x-intercepts: 1
enter the coordinates of the x-intercept: (?,?)
decide whether the function has extrema: no extrema
select a statement that describes the function: continually decreasing
identify the increasing or decreasing intervals.
interval increasing or decreasing

Explanation:

Step1: Find y - intercept

The y - intercept is the point where the graph intersects the y - axis. The y - axis is at \(x = 0\). From the graph, when \(x=0\), the point is \((0,0)\)? Wait, no, looking at the graph, the line passes through the origin? Wait, the graph has a vertical line at \(x = 0\)? Wait, no, the graph is a curve? Wait, the graph shown: the blue curve and the black vertical line? Wait, no, the function's graph: the y - intercept is where \(x = 0\). Looking at the grid, when \(x = 0\), the coordinate is \((0,0)\)? Wait, no, maybe I misread. Wait, the input field for y - intercept: let's check the graph. The graph crosses the y - axis at \((0,0)\)? Wait, no, the vertical line is \(x = 0\), and the curve: when \(x = 0\), the y - coordinate is 0? Wait, maybe the y - intercept is \((0,0)\)? Wait, no, let's see the graph again. The graph has a point at \(x = 0\), so the y - intercept is \((0,0)\)? Wait, but the input field is for coordinates. Wait, maybe the y - intercept is \((0,0)\).

Step2: Find x - intercept

The x - intercept is where \(y=0\). From the graph, the graph intersects the x - axis at \(x = 0\), so the x - intercept is \((0,0)\).

Step3: Check for extrema

The function is a curve that is continually decreasing, so it has no extrema (since it's always decreasing, no local max or min).

Step4: Decreasing interval

The function is continually decreasing, so the interval for decreasing is \((-\infty,\infty)\) (or all real numbers), and it's decreasing on that interval.

But let's focus on the y - intercept first. Wait, the y - intercept: when \(x = 0\), the point is \((0,0)\). So the coordinates of the y - intercept are \((0,0)\).

Answer:

For the y - intercept: \((0,0)\)
For the x - intercept: \((0,0)\)
For extrema: No extrema
For the function's description: Continually decreasing (already selected)
For the interval: The interval \((-\infty,\infty)\) is decreasing.