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: select choice
negative: select choice

Explanation:

Step1: Analyze x - intercept

The x - intercept is the point where the graph intersects the x - axis (where \(y = 0\)). Looking at the graph, the line is \(y=- 3\), which is parallel to the x - axis and never intersects the x - axis (since \(y=-3
eq0\) for all \(x\)). So, there is no x - intercept.

Step2: Analyze y - intercept

The y - intercept is the point where the graph intersects the y - axis (where \(x = 0\)). Substituting \(x = 0\) into the equation of the line (which is \(y=-3\)), we get the y - intercept at \((0,-3)\).

Step3: Analyze where the function is positive

A function is positive when \(y>0\). Since the equation of the line is \(y =- 3\), and \(-3<0\) for all \(x\), the function is never positive.

Step4: Analyze where the function is negative

A function is negative when \(y < 0\). Since \(y=-3\) and \(-3<0\) for all real values of \(x\), the function is negative for all real numbers \(x\) (i.e., for all \(x\) in \((-\infty,\infty)\)).

Answer:

x - intercept(s): None (the graph of \(y =-3\) does not intersect the x - axis)
y - intercept: \((0,-3)\)
positive: Never (the function \(y=-3\) is never greater than 0)
negative: For all real numbers \(x\) (or \((-\infty,\infty)\))