Question

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

Accepted Answer

Step 1: Identify the graph type. The graph shows a circle centered at (20, 10). A circle is defined by the equation $$(x - h)^2$ + (y - k)^2$ = r^2$, where (h$$, k)$$ is the center and r$ is the radius. Step 2: Determine if y$ is a function of x$. For y$ to be a function of x$, each x$-value must correspond to exactly one y$-value. In a circle, for many x$-values, there are two corresponding y$-values (one above and one below the center), so y$ is not a function of x$. Step 3: Find the domain of the relation. The domain is the set of all possible x$-values on the circle. Since the circle is centered at x=20$ and extends equally in both directions by the radius, the domain is $$[20 - r, 20 + r]$$. Step 4: Find the range of the relation. The range is the set of all possible y$-values on the circle. Since the circle is centered at y=10$ and extends equally in both directions by the radius, the range is $$[10 - r, 10 + r]$$. Step 5: Summarize: y$ is not a function of x$ because the vertical line test fails (vertical lines intersect the circle at two points). The domain and range are intervals centered at the circle's center coordinates, extending by the radius.

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Definition of a Function

Vertical Line Test

Domain and Range of a Relation