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Found in: Page 66

### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

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

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

See the step by step solution

## 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 $f\left(x\right)=mx+b$, where m and b are real numbers.

## Step 2 – Given information.

The given functions are:

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

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

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

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

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

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