Pre-Algebra Examples

$y = x + 2$

Step 1

Write $y = x + 2$ as a function.

$f (x) = x + 2$

Step 2

Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.

Largest Degree: $1$

Leading Coefficient: $1$

Step 3

Create a list of the coefficients of the function except the leading coefficient of $1$ .

$2$

Step 4

There will be two bound options, $b_{1}$ and $b_{2}$ , the smaller of which is the answer. To calculate the first bound option, find the absolute value of the largest coefficient from the list of coefficients. Then add $1$ .

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Step 4.1

Arrange the terms in ascending order.

$b_{1} = | 2 |$

Step 4.2

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$b_{1} = 2 + 1$

Step 4.3

Add $2$ and $1$ .

$b_{1} = 3$

Step 5

To calculate the second bound option, sum the absolute values of the coefficients from the list of coefficients. If the sum is greater than $1$ , use that number. If not, use $1$ .

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Step 5.1

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$b_{2} = 2$

Step 5.2

Arrange the terms in ascending order.

$b_{2} = 1, 2$

Step 5.3

The maximum value is the largest value in the arranged data set.

$b_{2} = 2$

Step 6

Take the smaller bound option between $b_{1} = 3$ and $b_{2} = 2$ .

Smaller Bound: $2$

Step 7

Every real root on $f (x) = x + 2$ lies between $- 2$ and $2$ .

$- 2$ and $2$