Interval Notation to Express Domain, Range, and Inequalities

​Interval Notation to Express Domain, Range, and Inequalities

By Ferdad Roidad

Multiple Choice

The inequality $$\left\{x:\ -8\le x<5\right\}$$ in interval notation is:

• $$\left(-8,\ 5\right]$$

• $$\left(-8,\ 5\right)$$

• $$\left[-8,\ 5\right)$$

• $$\left[-8,\ 5\right]$$

Inequalities

Compound Inequality

Interval notation for simple inequality

Multiple Choice

The domain for the linear function $$y=x$$ is the set of all real numbers.

What is the interval notation representation for the set of all real numbers?

Hint: Use desmos.com/calculator (graphing calculator) to view the graph of the function.

• $$\left[-\infty,\ \infty\right]$$

• $$\left(-\infty,\ \infty\right)$$

• $$\left(-\infty,\ 0\right]$$

• $$\left[0,\ 0\right]$$

Multiple Choice

The range for the absolute value function $$y=\left|x\right|$$ is:

HINT: Use desmos.com/calculator (graphing calculator) to view the graph of the function.

• $$\left(-\infty,\ \infty\right)$$

• $$\left(0,\ \infty\right)$$

• $$\left[0,\ \infty\right)$$

• $$\left(-\infty,\ 0\right)$$

Multiple Choice

The domain for the reciprocal function $$y=\frac{1}{x}$$ which is undefined when x = 0 is:

HINT: Use desmos.com/calculator (graphing calculator) to see the graph of the function.

• $$\left(-\infty,\ 0\right)$$

• $$\left(0,\ \infty\right)$$

• $$\left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$$

Multiple Choice

Which inequality represents the set of all real numbers which is represented as $$\left(-\infty,\ \infty\right)$$ in interval notation?

• $$\left\{x:\ x<0\ or\ x>0\right\}$$

• $$\left\{x:\ x<0\ or\ x\ \ge0\right\}$$

• $$\left\{x\ :\ x\ne0\right\}$$