Question

1. the graph of relation t is shown. which of the following shows the graph of t and its inverse?

Explanation:

Step1: Recall Inverse Graph Rule

The graph of a relation and its inverse are symmetric about the line \( y = x \) (the dashed line in the original graph). So, we need to check which option has the original relation (blue curve) and its inverse (other curve) symmetric over \( y = x \).

Step2: Analyze Each Option

• First option (with blue and orange curves): The blue curve is the original (from the first graph, a curve in the second quadrant, moving left). The orange curve should be its inverse, so we check symmetry over \( y = x \). If we reflect the blue curve over \( y = x \), the orange curve's shape and position should match the reflection. Looking at the first option's graph, the orange curve appears to be the reflection of the blue curve over \( y = x \) (since swapping \( x \) and \( y \) coordinates, the curve's orientation and position relative to \( y = x \) is symmetric).
• The other (partial) option doesn't show a clear symmetric pair. So the first option (with blue and orange curves) is correct.

Answer:

The graph with the blue curve (original relation) and the orange curve (its inverse) (the first option among the choices, showing two curves symmetric about \( y = x \)).