Question

Use the image to answer the question.

A curve is graphed on a coordinate plane. The plane’s x and y axes range from negative 2 to 2 in unit increments.

How many real and non-real solutions does the graphed equation have?

(1 point)
Responses

three real and zero non-real
three real and zero non-real

zero real and three non-real
zero real and three non-real

two real and one non-real
two real and one non-real

one real and one non-real
one real and one non-real
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Answer 1

To determine the number of real and non-real solutions of the graphed equation, you would need to analyze where the curve intersects the x-axis. Each point where the curve crosses the x-axis indicates a real solution.

1. **Three real and zero non-real**: The curve could intersect the x-axis at three distinct points.

2. **Zero real and three non-real**: The curve may not intersect the x-axis at all, indicating there are no real solutions and three complex (non-real) solutions.

3. **Two real and one non-real**: The curve could intersect the x-axis at two points while having one complex solution (which occurs if the polynomial degree is three).

4. **One real and one non-real**: The curve may intersect the x-axis once, with the other solution being complex.

Without the actual image, I cannot definitively determine how many intersections there are. However, by observing the graph of the curve, you can count the x-axis crossings to identify the number of real solutions.

Based on your observations of the graph:

- If it intersects at three points, select "three real and zero non-real."
- If it doesn’t intersect, go with "zero real and three non-real."
- If it intersects twice, choose "two real and one non-real."
- If it only intersects once, select "one real and one non-real."

Please review the graph and choose the appropriate response based on how many times the curve crosses the x-axis.