Questions: 3.2 Properties of a Function's Graph Question Completed: Which of the following statements is not true? Choose the incorrect statement. A. A function can have several y-intercepts. B. A function can have infinitely many x-intercepts C. Another name for an x-intercept is a real zero. D. Every function can be represented by a graph in the Cartesian plane.

Solution Steps

To determine which statement is not true, we need to analyze each statement based on the properties of functions and their graphs.

• A function can have only one $y$-intercept because it must pass the vertical line test.
• A function can have infinitely many $x$-intercepts, for example, the sine function.
• An $x$-intercept is indeed another name for a real zero.
• Not every function can be represented by a graph in the Cartesian plane, for example, functions that are not well-defined for all real numbers.

Based on this analysis, statement A is not true.

A function can have only one \( y \)-intercept because it must pass the vertical line test. If a function had more than one \( y \)-intercept, it would not be a function.

A function can have infinitely many \( x \)-intercepts. For example, the sine function \( \sin(x) \) has infinitely many \( x \)-intercepts at \( x = n\pi \) where \( n \) is an integer.

An \( x \)-intercept is indeed another name for a real zero. This is because at the \( x \)-intercept, the function value is zero.

Not every function can be represented by a graph in the Cartesian plane. For example, functions that are not well-defined for all real numbers or functions that are defined in higher dimensions cannot be represented in the Cartesian plane.

Final Answer