Chapter SH, Problem 9.7.8EP

To determine

The representation of the equation $y={\left(-2\right)}^x$ is either linear or non-linear is to be analyze.

Answer to Problem 9.7.8EP

The eq. $y={\left(-2\right)}^x$ shows the representation of the non-linear function

Explanation of Solution

Given:

  $y={\left(-2\right)}^x$

Concept Used:

In mathematics, a polynomial equation of the one degree that can be put in the form of the equation $f\left(x\right)=mx+b$ , then the function is known as the linear function. The graph of the linear function is always straight line.

A mathematical system of equation which is combine form of two or more variables which contains at least one equation which is not linear is known as the non-linear function.

The given equation cannot be written in the from the straight line eq. as there is exponent of the $\left(-2\right)$ is $x$ . One cannot write this eq. in the slope-intercept from to get the value of the slope and the $y-$ intercept value to analyze as linear function.

Hence, the given eq. shows the representation of the non-linear function.

Conclusion:

Hence, $y={\left(-2\right)}^x$ is non-linear function.