Chapter 5, Problem 1P

To determine

To plot:

The function $f\left(x\right)=\frac{x^2-3x+7}{\sqrt{2x+5}}$ for $-1\le x\le 5$ by using $\text{plot}$ command.

Answer to Problem 1P

Solution:

The plot of the function $f\left(x\right)=\frac{x^2-3x+7}{\sqrt{2x+5}}$ for $-1\le x\le 5$ is stated as follows.

Explanation of Solution

The given function is,

$f\left(x\right)=\frac{x^2-3x+7}{\sqrt{2x+5}}$

The range of the function is $-1\le x\le 5$.

Substitute $x=-1$ in the above equation.

$\begin{array}{c}f\left(x\right)=\frac{x^2-3x+7}{\sqrt{2x+5}}\\ =\frac{{\left(-1\right)}^2-3\left(-1\right)+7}{\sqrt{2\left(-1\right)+5}}\\ =\text{6}\text{.3509}\end{array}$

Substitute $x=5$ in the above equation.

$\begin{array}{c}f\left(x\right)=\frac{x^2-3x+7}{\sqrt{2x+5}}\\ =\frac{{\left(5\right)}^2-3\left(5\right)+7}{\sqrt{2\left(5\right)+5}}\\ =\text{4}\text{.3894}\end{array}$

The value of $f\left(x\right)$ lies from $\text{6}\text{.3509}\le f(x)\le \text{4}\text{.3894}$.

Write the MATLAB script to plot the function $f\left(x\right)=\frac{x^2-3x+7}{\sqrt{2x+5}}$ for $-1\le x\le 5$.

MATLAB Code:

x = [-1:0.01:5];

% Define the vector x.

fx = (x.^2-3*x+7)./sqrt(2*x+5);

% Define the function fx.

plot(x,fx,'-g')

Save the MATLAB script with the name, Chapter5_29864_5_1P.m in the current folder. Execute the script by typing the script name at the command window to get the plot of the function $f\left(x\right)=\frac{x^2-3x+7}{\sqrt{2x+5}}$ for $-1\le x\le 5$.

Result:

Conclusion:

The plot of the function $f\left(x\right)=\frac{x^2-3x+7}{\sqrt{2x+5}}$ for $-1\le x\le 5$ is stated above.