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Q24.

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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

Which of the functions $f (x) = 2 x + 4, g (x) = 7$ and $h (x) = x^{3} - x^{2} + 3 x$ is not linear.

The function $h (x) = x^{3} - x^{2} + 3 x$ is not a linear function.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 – Definition of a linear equation and linear function.

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 functions are:

$\begin{matrix} f (x) = 2 x + 4 \\ g (x) = 7 \\ h (x) = x^{3} - x^{2} + 3 x \end{matrix}$

Step 3 – Check whether the equation is linear or not.

The given function $f (x) = 2 x + 4$ is in the form of $f (x) = m x + b$ , where both m=2 and b=4 are real values. So, the function $f (x) = 2 x + 4$ is a linear function.

The given function $g (x) = 7$ is a constant function and a constant function is always a linear function. So, the function $g (x) = 7$ is a linear function.

The given function $h (x) = x^{3} - x^{2} + 3 x$ is not a linear function because the exponent of $x$ is other than 1.

Thus, the function $h (x) = x^{3} - x^{2} + 3 x$ is not a linear function.

Most popular questions for Math Textbooks

Solve each inequality.

$| x + 4 | > 2$

Find each value if $f (x) = 5 x - 9$

$f (y)$

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

$y = \sqrt{2 x - 5}$

Graph the line passing through the given point with the given slope

$(-2,2),- \frac{1}{3}$

Write each equation in standard form. Identify A, B and C.

$0.5 x = 3$

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