The x-axis goes from negative 6 to 6 and the y-axis goes from negative 6 to 6. A function labeled f left-parenthesis x right-parenthesis has points left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 1 comma 3 right-parenthesis, and left-parenthesis 3 comma 5 right-parenthesis. Starting from the point left-parenthesis 0 comma 1 right-parenthesis the graph curves right and up and then up and right. A second function labeled g left-parenthesis x right-parenthesis has points left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 1 comma 3 right-parenthesis, and left-parenthesis 3 comma 5 right-parenthesis. Starting from the point left-parenthesis 0 comma 1 right-parenthesis the graph curves up and right and then right and up. A third function labeled h left-parenthesis x right-parenthesis has points left-parenthesis 1 comma 0 right-parenthesis, left-parenthesis 3 comma 1 right-parenthesis, and left-parenthesis 5 comma 3 right-parenthesis. Starting from the point left-parenthesis 1 comma 0 right-parenthesis the graph curves up and right and then right and up. Question Use the graph to answer the question. Which function, g or h, is the inverse of function f, and why? (1 point) Responses The function h is the inverse because h and f intersect at one, and only one, point. The function h is the inverse because h and f intersect at one, and only one, point. The function h is the inverse because for every point on the graph of f, there is a corresponding point on the graph of h. The function h is the inverse because for every point Image with alt text: left-parenthesis x comma y right-parenthesis on the graph of f , there is a corresponding point Image with alt text: left-parenthesis y comma x right-parenthesis on the graph of h . The function g is the inverse because for every point on the graph of f, there is a corresponding point on the graph of g. The function g is the inverse because for every point Image with alt text: left parenthesis a comma b right parenthesis on the graph of f , there is a corresponding point Image with alt text: left parenthesis b comma a right parenthesis on the graph of g . The function g is in the inverse because g and f intersect at multiple points.
The function h is the inverse because h and f intersect at one, and only one, point.
The correct answer is: The function g is the inverse because for every point on the graph of f, there is a corresponding point on the graph of g.
To determine which function, g or h, is the inverse of function f, we need to understand the concept of inverse functions.
Two functions, f and g, are inverses of each other if applying one function to the output of the other function results in the original input value. In other words, if f(g(x)) = x and g(f(x)) = x for all possible input values, then f and g are inverses.
Looking at the given information, we have three functions: f, g, and h. We need to find the function that is the inverse of function f.
The graph of function f starts at the point (0, 1) and curves right and up, then up and right. The graph of function g also starts at (0, 1) but curves up and right, then right and up. On the other hand, the graph of function h starts at (1, 0) and curves up and right, then right and up.
To determine the inverse, we need to find a function that, when applied to the points of function f, produces the same result as applying the inverse function to the points of function f. In other words, for each point (x, y) on the graph of function f, there must be a corresponding point (y, x) on the graph of function h or g.
Analyzing the points (0, 1), (1, 3), and (3, 5) given for function f, we can see that when we swap the x and y coordinates, we get the corresponding points on the graph of function h, namely (1, 0), (3, 1), and (5, 3).
Since the points (0, 1), (1, 3), and (3, 5) on the graph of function f correspond to the points (1, 0), (3, 1), and (5, 3) on the graph of function h, we can conclude that function h is the inverse of function f.
Therefore, the correct answer is: The function h is the inverse because h and f intersect at one, and only one, point.