Question

which graph shows a function and its inverse?
a.
graph a
b.
graph b
c.
graph c

Explanation:

To determine which graph shows a function and its inverse, we use the property that the graph of a function and its inverse are symmetric about the line \( y = x \). Let's analyze each option:

• Option A: The two lines (red and blue) do not appear to be symmetric about \( y = x \). Their slopes and intercepts don't reflect the inverse relationship.
• Option B: The red and blue lines also lack symmetry about \( y = x \). Their slopes and orientations don't align with the inverse function property.
• Option C: The red and blue lines are symmetric about the line \( y = x \). This matches the property of a function and its inverse, as reflecting a function over \( y = x \) gives its inverse.

Answer:

C. (The graph in option C shows a function and its inverse, as the two lines are symmetric about \( y = x \).)