Answer:
Explanation:
To determine which table represents the output y as a function of the input x, we need to check if each input value x corresponds to a unique output value y. In a function, each input can only have one output. Looking at table a, we see that the input values -50, -25, -15, and 0 have different output values. However, the input value 10 corresponds to two different output values (20 and 30). Therefore, table a does not represent a function. Table b also does not represent a function because the input value 0 corresponds to two different output values (7 and 4). Table c, on the other hand, does represent a function. Each input value has a unique output value, and there are no repeating input-output pairs. So, table c represents the output y as a function of the input x because it satisfies the definition of a function: each input has a unique output. 2) A graph is said to be one-to-one if each input value corresponds to a unique output value, and no two input values correspond to the same output value. In other words, a one-to-one graph does not have any repeating points. To determine if a graph is one-to-one, we can use the horizontal line test. The horizontal line test involves drawing horizontal lines across the graph and checking if each horizontal line intersects the graph at most once. If every horizontal line intersects the graph at most once, then the graph is one-to-one. However, if any horizontal line intersects the graph more than once, then the graph is not one-to-one. 3) The equation of a circle with radius 5 and center (h, k) is given by the formula: (x - h)^2 + (y - k)^2 = r^2 where (x, y) represents any point on the circle. In this case, the center of the circle is (3, -2) and the radius is 5. Plugging these values into the equation, we have: (x - 3)^2 + (y - (-2))^2 = 5^2 Simplifying the equation, we get: (x - 3)^2 + (y + 2)^2 = 25 So, the equation of the circle with radius 5 and center (3, -2) is (x - 3)^2 + (y + 2)^2 = 25. 4) To find the domain and range of a graph, we need to determine the set of all possible input values (domain) and the set of all possible output values (range). Looking at the graph provided, we see that the input values extend from -5 to 3, including both endpoints. So, the domain of the graph is the interval [-5, 3]. For the range, we observe that the output values extend from -2 to 2, including both endpoints. Therefore, the range of the graph is the interval [-2, 2]. In interval notation, the domain is [-5, 3] and the range is [-2, 2]