Answer :
To determine the type of function where each y-value has more than one corresponding x-value, let's examine each option carefully:
A. Nonlinear Function: This option refers to the type of function based on its graph. Nonlinear functions are those whose graphs are not a straight line. These could take many forms such as quadratic, cubic, exponential, etc. This definition does not specifically address the relationship between x and y values regarding multiple correspondences.
B. Many-to-One Function: This option describes a function where each y-value can be associated with more than one x-value. This means that for different values of x, the function can yield the same y value.
C. One-to-One Function: This option describes a function where each y-value has exactly one corresponding x-value. In other words, no y-value will be repeated for different x-values. Therefore, it is the opposite of what we are looking for.
D. Linear Function: This option typically refers to functions of the form [tex]\(y = mx + b\)[/tex], where the graph is a straight line. While linear functions can be either one-to-one or many-to-one depending on the slope [tex]\(m\)[/tex], this definition does not specifically address the relationship mentioned in the question.
Based on these analyses, the correct answer is:
B. Many-to-One Function
A. Nonlinear Function: This option refers to the type of function based on its graph. Nonlinear functions are those whose graphs are not a straight line. These could take many forms such as quadratic, cubic, exponential, etc. This definition does not specifically address the relationship between x and y values regarding multiple correspondences.
B. Many-to-One Function: This option describes a function where each y-value can be associated with more than one x-value. This means that for different values of x, the function can yield the same y value.
C. One-to-One Function: This option describes a function where each y-value has exactly one corresponding x-value. In other words, no y-value will be repeated for different x-values. Therefore, it is the opposite of what we are looking for.
D. Linear Function: This option typically refers to functions of the form [tex]\(y = mx + b\)[/tex], where the graph is a straight line. While linear functions can be either one-to-one or many-to-one depending on the slope [tex]\(m\)[/tex], this definition does not specifically address the relationship mentioned in the question.
Based on these analyses, the correct answer is:
B. Many-to-One Function
