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Q18.

Expert-verified

Algebra 2

Found in: Page 66

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.

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

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 – 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.

Step 2 – Given information.

The given function is:

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

Step 3 – 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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