Find the domain and range of the relation and determine whether it is a function.
Question 4 graphA graph with horizontal axis x range from left to right labeled is negative 4 to 4; vertical axis y labeled from top to bottom is range from 4 to negative 4.
The graph shows an upward going curve starting from around left parenthesis 1 comma 0 right parenthesis. The curve goes toward the left sharply upward close along the right side of vertical asymptote x equals negative 2.
(1 point)
Responses
domain: positive integers; range: positive integers; No, it is not a function.
domain: positive integers; range: positive integers; No, it is not a function.
domain: x ≥ 0; range: y > –2; No, it is not a function.
domain: x ≥ 0; range: y > –2; No, it is not a function.
domain: all real numbers; range: all real numbers; Yes, it is a function.
domain: all real numbers; range: all real numbers; Yes, it is a function.
domain: x > –2; range: y > 0; Yes, it is a function.
The correct answer is:
domain: all real numbers; range: all real numbers; Yes, it is a function.
Which graph represents a function?
(1 point)
Responses
Graph 5aThe circle passes through the points left-parenthesis 0 comma 7 right-parenthesis, left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis negative 1 comma 0 right-parenthesis, left-parenthesis negative 7 comma 0 right-parenthesis, left-parenthesis negative 7 comma 8 right-parenthesis, and left-parenthesis negative 8 comma 7 right-parenthesis.
Image with alt text: Graph 5a The circle passes through the points left-parenthesis 0 comma 7 right-parenthesis, left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis negative 1 comma 0 right-parenthesis, left-parenthesis negative 7 comma 0 right-parenthesis, left-parenthesis negative 7 comma 8 right-parenthesis, and left-parenthesis negative 8 comma 7 right-parenthesis.
Graph 5bThe parabola opens to the right. It has a vertex at left-parenthesis 0 comma 0 right-parenthesis and is symmetric about the positive x-axis. It passes through the points left-parenthesis 4 comma 2 right-parenthesis and left-parenthesis 4 comma negative 2 right-parenthesis.
Image with alt text: Graph 5b The parabola opens to the right. It has a vertex at left-parenthesis 0 comma 0 right-parenthesis and is symmetric about the positive x-axis. It passes through the points left-parenthesis 4 comma 2 right-parenthesis and left-parenthesis 4 comma negative 2 right-parenthesis.
Graph 5cThe parabola opens downward. It has a vertex at left-parenthesis 0 comma 2 right-parenthesis and is symmetric about the y-axis. It passes through the points left-parenthesis negative 2 comma negative 1 right-parenthesis and left-parenthesis 2 comma negative 1 right-parenthesis.
Image with alt text: Graph 5c The parabola opens downward. It has a vertex at left-parenthesis 0 comma 2 right-parenthesis and is symmetric about the y-axis. It passes through the points left-parenthesis negative 2 comma negative 1 right-parenthesis and left-parenthesis 2 comma negative 1 right-parenthesis.
Graph 5d
The correct answer is:
Graph 5b
The correct answer is:
domain: all real numbers; range: all real numbers; Yes, it is a function.
To find the domain and range of a relation, you can examine the x-values and y-values shown in the graph. The domain refers to the set of all possible x-values, while the range refers to the set of all possible y-values.
Looking at the given graph, the x-values range from -4 to 4, as labeled on the horizontal axis. Therefore, the domain of the relation is -4 ≤ x ≤ 4 or, since x can also take any real number, you can also say the domain is all real numbers.
Similarly, the y-values range from 4 to -4, as labeled on the vertical axis. Therefore, the range of the relation is -4 ≤ y ≤ 4 or, since y can also take any real number, you can also say the range is all real numbers.
Now, to determine whether the relation is a function or not, you need to check if there are any vertical lines that intersect the graph at more than one point. If there are no such vertical lines, then the relation is a function. However, if there is at least one vertical line that intersects the graph at more than one point, then the relation is not a function.
From the given graph description, it mentions that the curve sharply goes upward close along the right side of the vertical asymptote x = -2. This suggests that there could be multiple y-values for the same x-value near the vertical asymptote. Therefore, the relation is not a function.
Hence, the correct answer is: domain: all real numbers; range: all real numbers; No, it is not a function.