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
(type your answer in interval notation.)
(b) select the correct choice and, if necessary, fill in the answer box to complete your choice.
a. the intercept(s) is/are (2,0),(6,0),(0,12). (type an ordered pair. use a comma to separate answers as needed.)
b. there are no intercepts.
(c) select all that apply.
a. it is symmetric with respect to the y - axis.
b. it is symmetric with respect to the origin.
c. it is symmetric with respect to the x - axis.
d. the graph has no symmetry.

Explanation:

Step1: Check if it's a function

Apply vertical - line test. Since any vertical line intersects the graph at most once, it is a function.

Step2: Find domain and range

The graph extends horizontally from $x = 0$ to $x = 8$. So the domain is $[0,8]$. Vertically, it extends from $y=-4$ to $y = 12$. So the range is $[-4,12]$.

Step3: Identify intercepts

The x - intercepts are the points where the graph crosses the x - axis, which are $(2,0)$ and $(6,0)$. The y - intercept is the point where the graph crosses the y - axis, which is $(0,12)$. So the intercepts are $(2,0),(6,0),(0,12)$.

Step4: Check for symmetry

If we rotate the graph 180 degrees about the origin, it does not map onto itself. If we reflect it over the y - axis, it does not map onto itself. If we reflect it over the x - axis, it does not map onto itself. So the graph has no symmetry.

Answer:

(a) Domain: $[0,8]$, Range: $[-4,12]$
(b) A. The intercept(s) is/are $(2,0),(6,0),(0,12)$
(c) D. The graph has no symmetry.