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Linear and Nonlinear Functions Overview

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Questions and Answers

What is the main difference between linear and nonlinear functions?

Linear functions have a variable slope, while nonlinear functions have a constant slope.

Linear functions have exponents higher than 1, while nonlinear functions have exponents equal to or less than 1.

Linear functions always have a y-intercept, while nonlinear functions never have a y-intercept.

Linear functions form a straight line on a graph, while nonlinear functions form a curve. (correct)

Which type of function forms a curve when plotted on a graph?

Linear function

Nonlinear function (correct)

Function with high exponents

Function with a constant slope

What characteristic of a linear function ensures the slope is constant?

Forming a straight line on a graph (correct)

Forming a curve on a graph

Having no y-intercept

Having a high exponent

In which type of function can the equation be written in the form y = mx + c?

Linear function Signup and view all the answers

What is a distinguishing feature of nonlinear functions in terms of exponents?

They always have exponents greater than 1. Signup and view all the answers

Why is it easier to determine if a function is linear by looking at its graph?

Linear functions always form straight lines on graphs. Signup and view all the answers

What aspect of the equation y = mx + c helps identify a linear function?

'm' and 'c' being constants Signup and view all the answers

What is the best way to find the y-intercept of a line?

Insert x = 0 into the formula Signup and view all the answers

In a nonlinear function, why is the slope not constant?

Because it has changing slopes at different points on the curve Signup and view all the answers

When is an equation classified as linear?

When the degree of the equation is 1 Signup and view all the answers

Which type of equation forms a straight line graph?

Linear equation Signup and view all the answers

What characteristic defines a polynomial?

Consists of many terms with positive integer exponents Signup and view all the answers

What happens when the highest exponent in a polynomial is 2?

It forms a curve known as a parabola Signup and view all the answers

Why is Example 4 considered a nonlinear graph?

Because x has a power of 4 in the equation Signup and view all the answers

What distinguishes linear and nonlinear equations based on their degrees?

The highest power (exponent) of x in the equation Signup and view all the answers