Question

from the graph, determine the x - and y - intercepts and the vertical and horizontal asymptotes. (if an answer does not exist, enter dne. enter
x - intercept
(x, y) = (
) (smaller x - value)
x - intercept
(x, y) = (
) (larger x - value)
y - intercept
(x, y) = (
)
vertical asymptote(s)

horizontal asymptote

Explanation:

Step1: Find x - intercepts

The x - intercepts are the points where the graph crosses the x - axis (\(y = 0\)).
Looking at the graph, the points are \((-1,0)\) and \((1,0)\). Since \(-1<1\), the smaller \(x\) - value is \(-1\) and the larger \(x\) - value is \(1\).

Step2: Find y - intercept

The y - intercept is the point where the graph crosses the y - axis (\(x = 0\)).
Looking at the graph, when \(x = 0\), \(y=-1\). So the y - intercept is \((0,-1)\).

Step3: Find vertical asymptotes

Vertical asymptotes are the vertical lines \(x = a\) where the function approaches infinity or negative infinity as \(x\) approaches \(a\).
Looking at the graph, the vertical asymptotes are \(x=-2\) and \(x = 2\).

Step4: Find horizontal asymptotes

Horizontal asymptotes are the horizontal lines \(y = b\) that the function approaches as \(x\to\pm\infty\).
Looking at the graph, as \(x\to\pm\infty\), \(y = 1\). So the horizontal asymptote is \(y = 1\).

Answer:

\(x\) - intercept (smaller \(x\) - value): \((-1,0)\)
\(x\) - intercept (larger \(x\) - value): \((1,0)\)
\(y\) - intercept: \((0,-1)\)
Vertical asymptote(s): \(x=-2,x = 2\)
Horizontal asymptote: \(y = 1\)