The graph of the polynomial function P(x) is shown.
a. List the real zeros of P(x).
b. List the turning points of P(x).
c. State the left and right behavior of P(x).
To answer this question, you'll need to analyze the graph of the polynomial function P(x). Let's go step by step to find the real zeros, turning points, and the left and right behavior of P(x).
a. Real Zeros:
The real zeros of a polynomial function are the values of x for which the function equals zero. On the graph, look for points where the function intersects the x-axis. These points represent the x-values where P(x) = 0. Note them down as the real zeros of P(x).
b. Turning Points:
The turning points of a polynomial function occur where the graph changes from increasing to decreasing or from decreasing to increasing. These points are also known as local maxima or minima. Examine the highest and lowest points on the graph and identify the corresponding x-values as the turning points of P(x).
c. Left and Right Behavior:
The left behavior of P(x) refers to the trend or direction of the graph as x approaches negative infinity. Likewise, the right behavior refers to the trend as x approaches positive infinity. Observe how the graph approaches these extreme ends and describe the behavior of P(x).
By following these steps, you should be able to answer parts a, b, and c of the question. Just remember to visually analyze the graph to obtain the necessary information.