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Q18.

Expert-verifiedFound in: Page 66

Book edition
Middle English Edition

Author(s)
Carter

Pages
804 pages

ISBN
9780079039903

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

** **

**$h\left(x\right)=2{x}^{3}-4{x}^{2}+5$**

**No**, the function $h\left(x\right)=2{x}^{3}-4{x}^{2}+5$ is not a 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 $f\left(x\right)=mx+b$, where m and b are real numbers.

The given function is:

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

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

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

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

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