Question

use the graph to estimate the x- and y-intercepts of the function and describe where the function is positive and negative.
x-intercept(s): select choice
y-intercept: select choice
positive: when select choice
negative: when select choice

Explanation:

Step1: Identify x - intercepts

The x - intercepts are the points where the graph intersects the x - axis (where \(y = 0\)). From the graph, we can see that the line crosses the x - axis at \(x=-1\) and \(x = 3\) (assuming the grid has integer coordinates and we estimate the intersection points). So the x - intercepts are \((-1,0)\) and \((3,0)\).

Step2: Identify y - intercept

The y - intercept is the point where the graph intersects the y - axis (where \(x = 0\)). Looking at the graph, when \(x = 0\), the value of \(y\) is \(2\) (estimating from the grid), so the y - intercept is \((0,2)\).

Step3: Determine where the function is positive

A function is positive when its graph is above the x - axis (\(y>0\)). From the graph, the function is above the x - axis between the two x - intercepts, i.e., when \(-1

Step4: Determine where the function is negative

A function is negative when its graph is below the x - axis (\(y < 0\)). From the graph, the function is below the x - axis when \(x<-1\) or \(x>3\).

Answer:

x - intercept(s): \((-1,0)\) and \((3,0)\)
y - intercept: \((0,2)\)
positive: when \(-1 < x < 3\)
negative: when \(x < - 1\) or \(x>3\)