Which of the following graphs represents a function that is not one-to-one?
Practice Questions
Q1
Which of the following graphs represents a function that is not one-to-one?
A straight line with a positive slope.
A parabola opening upwards.
A horizontal line.
A line with a negative slope.
Questions & Step-by-Step Solutions
Which of the following graphs represents a function that is not one-to-one?
Step 1: Understand what a function is. A function is a relationship where each input has exactly one output.
Step 2: Learn what 'one-to-one' means. A one-to-one function means that each output is produced by only one input.
Step 3: Know the 'horizontal line test.' This test checks if a function is one-to-one. If a horizontal line crosses the graph more than once, the function is not one-to-one.
Step 4: Identify the shape of a parabola that opens upwards. It looks like a 'U' shape.
Step 5: Draw a horizontal line across the parabola. Notice that the line can intersect the parabola at two points.
Step 6: Conclude that since the horizontal line intersects the parabola at two points, the parabola is not a one-to-one function.
