Question

When figuring out if a graph is a non- linear function, you need to determine if it's really a function by A. checking to see if each x-value is unique B. checking to see if each y-value is unique.

Answer 1

To confirm if a graph represents a non-linear function, check if it passes the vertical line test to ensure it's a function, and then verify if the graph is not a straight line, indicating non-linearity. Linear functions have the form y = mx + b with a constant slope, while non-linear functions have curves or varying slopes.

Step-by-step explanation:

To determine if a graph is a non-linear function, we need to first confirm that it is a function. One way to do this is by checking to see if each x-value is paired with exactly one y-value, which is known as the vertical line test. However, the uniqueness of y-values is not a proper test for a function, as multiple x-values can be associated with the same y-value in many functions.

A linear function can be identified by its graph, which is a straight line and can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept. In contrast, non-linear functions will have graphs that are not straight lines; they could have curves, peaks, and different slopes at various points.

For example, a linear equation such as y = 2x + 1 will produce a straight line when plotted on a graph, while a non-linear function such as y = x^2 will show a parabolic curve.

Answer 2

To determine if a graph is a non-linear function, A. check if each x-value is unique.

Step-by-step explanation:

A non-linear function is a mathematical relationship that does not follow a straight-line trajectory. Unlike linear functions, which have a constant rate of change, non-linear functions exhibit varying rates. Their graphs often display curves, arcs, or other complex shapes, reflecting changing degrees of influence between input and output variables across different ranges.

To determine if a graph is a non-linear function, you need to check if each x-value is unique. If each x-value is unique, then it is a function. This is because in a function, each x-value maps to only one y-value. If there are repeated x-values, then it is not a function.