Q24. - Algebra 2

Question

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.

Step-by-Step Solution

Answer

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

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.