Question

determine whether the graph is that of a function by using the vertical-line test. in either case, use the graph to find the following.

(a) the domain and range
(b) the intercepts, if any
(c) any symmetry with respect to the x-axis, y-axis, or the origin

Explanation:

Determine if the graph represents a function

$$ \text{Every vertical line intersects the graph at most once} \implies \text{It is a function.} $$

Find the domain and range

$$
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$$

Find the intercepts and symmetry

$$
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$$

Answer:

Question 1

The graph represents a function because it passes the vertical-line test.

Question 2

The domain is \([-5, 0]\) and the range is \([-3, 2]\).

Question 3

The x-intercept is \((-4, 0)\) and the y-intercept is \((0, -3)\).

Question 4

The graph has no symmetry with respect to the x-axis, y-axis, or the origin.