Question

inverse relations and functions
the graph of relation c is shown.
which of the following is the graph of the relation and its inverse?
a.
image of graph a
b.
image of graph b
c.
image of graph c
check answer

Explanation:

Step1: Recall the property of inverse relations

The graph of a relation and its inverse are reflections of each other over the line \( y = x \). This means that if we have a point \((a, b)\) on the original relation, the point \((b, a)\) should be on its inverse, and this corresponds to reflecting over \( y = x \).

Step2: Analyze each option

• For Option A: The two curves (blue and red) do not appear to be reflections over \( y = x \). Their shapes and positions relative to the line \( y = x \) (the dashed line in the original relation's graph) do not match the reflection property.
• For Option B: Similarly, the blue and red curves here do not show the reflection over \( y = x \). The symmetry is not with respect to the line \( y = x \).
• For Option C: The red curve is the reflection of the blue curve over the line \( y = x \). If we imagine folding the graph along \( y = x \), the blue and red curves would coincide, which is the property of a relation and its inverse.

Answer:

C. (The graph where the red curve is the reflection of the blue curve over the line \( y = x \))