The x-axis goes from negative 10 to 10 and the y-axis goes from negative 10 to 10. A function labeled f is the right half of a parabola with vertex left-parenthesis negative 5 comma 0 right-parenthesis. A function labeled g starts at point left-parenthesis 0 comma negative 5 right-parenthesis and curves up to the right. A function labeled h starts at point left-parenthesis 5 comma 0 right-parenthesis and curves down to the right. Question Use the graph to answer the question. Which function, g or h, is the inverse function for function f? (1 point) Responses the function g because the graphs of f and g are symmetrical about the x-axis the function g because the graphs of f and g are symmetrical about the x -axis the function g because the graphs of f and g are symmetrical about the line y = x the function g because the graphs of f and g are symmetrical about the line y = x the function h because the graphs of f and h are symmetrical about the line y = x the function h because the graphs of f and h are symmetrical about the line y = x the function h because the graphs of f and h are symmetrical about the x-axis
The correct answer is: the function h because the graphs of f and h are symmetrical about the y = x line.
The correct answer is:
The function g because the graphs of f and g are symmetrical about the x-axis.
To determine which function, g or h, is the inverse function for function f, we need to consider the symmetry of their graphs with respect to either the x-axis or the line y = x.
Looking at the given information, we know that f is the right half of a parabola with a vertex at (-5, 0). This means that the graph of f is not symmetrical about the x-axis, as it only covers the right side. Therefore, we can eliminate the options that mention symmetry about the x-axis.
Next, we need to determine whether the graphs of f and g are symmetrical about the line y = x or if the graphs of f and h are symmetrical about the line y = x.
Since f is a right half of a parabola, it has a vertical axis of symmetry. The vertical axis of symmetry is a vertical line that passes through the vertex of the parabola and divides it into two equal halves. In this case, the axis of symmetry is the line x = -5.
Now, let's examine the graphs of g and h.
- Function g starts at (0, -5) and curves up to the right. This means its graph is not symmetrical about the line y = x, as it does not mirror the right half of f.
- Function h starts at (5, 0) and curves down to the right. This means its graph is also not symmetrical about the line y = x, as it does not mirror the right half of f.
Therefore, neither g nor h is the inverse function for function f. The correct answer is none of the given options.