Chapter 2: Q18. (page 66)

State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.
$h (x) = 2 x^{3} - 4 x^{2} + 5$

Short Answer

Expert verified

No, the function $h (x) = 2 x^{3} - 4 x^{2} + 5$ is not a linear function.

Step by step solution

– Definition of a linear equation and linear function.

In a linear equation the exponent of each variable is 1 and the variables may not be multiplied together. The graph of a linear equation is always a line.

In a linear function, each input value has a unique output value. In other words, for each point in domain, there is a unique value in the range of function. It can be written as $f (x) = m x + b$ , where m and b are real numbers.

– Given information.

The given function is:

$h (x) = 2 x^{3} - 4 x^{2} + 5$

– Check whether the equation is linear or not.

In the given function the highest exponent of x is 3.

The function $h (x) = 2 x^{3} - 4 x^{2} + 5$ is not a linear function because x has an exponent other than 1.

Thus,the required answer is “No” because the function $h (x) = 2 x^{3} - 4 x^{2} + 5$ is not a linear function.

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State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.
$h (x) = 2 x^{3} - 4 x^{2} + 5$

Short Answer

Step by step solution

– Definition of a linear equation and linear function.

– Given information.

– Check whether the equation is linear or not.

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State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.h(x)=2x3-4x2+5

Short Answer

Step by step solution

– Definition of a linear equation and linear function.

– Given information.

– Check whether the equation is linear or not.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Probability and Statistics

Mechanics Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.
$h (x) = 2 x^{3} - 4 x^{2} + 5$