Question

a) determine whether the graph illustrated represents a function
b) give the domain and range of each function or relation
c) determine the y - value(s) in the range that correspond to x = - 2
d) determine the x - value(s) in the domain that correspond to y = - 2

a) does the graph represent a function?
a. no, because a vertical line can be drawn to intersect the graph at more than one point.
b. no, because a vertical line cannot be drawn to intersect the graph at more than one point.
c. yes, because a vertical line cannot be drawn to intersect the graph at more than one point.
d. yes, because a vertical line can be drawn to intersect the graph at more than one point.

b) give the domain and range of the given function or relation
the domain is
(type your answer in interval notation.)
the range is
(type your answer in interval notation.)
c) list the value(s) of y that corresponds to x = - 2
(use a comma to separate answers as needed.)
d) list the value(s) of x that corresponds to y = - 2
(use a comma to separate answers as needed.)

Explanation:

Step1: Analyze Part (a)

To determine if a graph represents a function, we use the vertical line test. A graph represents a function if no vertical line intersects the graph at more than one point. Looking at the graph (a line), any vertical line will intersect it at most once. So the correct option is C: Yes, because a vertical line cannot be drawn to intersect the graph at more than one point.

Step2: Analyze Part (b)

Domain:

The domain of a graph is the set of all x - values the graph covers. From the graph, the left - most point has an x - coordinate of - 6 and the right - most point has an x - coordinate of 4. So the domain in interval notation is $[-6,4]$.

Range:

The range of a graph is the set of all y - values the graph covers. The top - most point has a y - coordinate of 6 and the bottom - most point has a y - coordinate of - 4. So the range in interval notation is $[-4,6]$.

Step3: Analyze Part (c)

To find the y - value when $x=-2$, we look at the graph. When $x = - 2$, we find the corresponding y - coordinate on the line. From the graph, when $x=-2$, $y = 2$.

Step4: Analyze Part (d)

To find the x - value when $y=-2$, we look at the graph. We find the point(s) on the line where $y=-2$ and then find the corresponding x - coordinate. From the graph, when $y = - 2$, $x = 2$.

Answer:

a) C. Yes, because a vertical line cannot be drawn to intersect the graph at more than one point.
b) Domain: $[-6,4]$, Range: $[-4,6]$
c) 2
d) 2