The image displays a graph of a function. What are the approximate coordinates of the local extrema and the y-intercept?

Analysis of the Graph

The graph shows a function \( y = f(x) \) plotted on a Cartesian coordinate system. The grid lines represent units on both the x and y axes.

Key Features Identified:

• Y-intercept: The graph intersects the y-axis at approximately \( (0, 1) \).
• Local Maximum: There is a local maximum around \( x = -2 \). The approximate coordinates are \( (-2, 2.5) \).
• Local Minimum 1: There is a local minimum around \( x = 1 \). The approximate coordinates are \( (1, 0.5) \).
• Local Minimum 2 (or inflection point with horizontal tangent): There is a local minimum (or a point where the tangent is horizontal) around \( x = 3 \). The approximate coordinates are \( (3, -1.5) \).
• X-intercepts: The graph crosses the x-axis at approximately \( x = -4.5 \), \( x = -1 \), and \( x = 5 \).
• Labeled points: The graph indicates \( -6 \) on the x-axis and \( 1 \) on the y-axis. It also shows \( 0 \) at the origin and \( 6 \) on the x-axis.

Approximated Local Extrema and Y-intercept:

• Local Maximum: Approximately \( (-2, 2.5) \)
• Local Minimum: Approximately \( (1, 0.5) \) and \( (3, -1.5) \)
• Y-intercept: Approximately \( (0, 1) \)