Domain Interval Notation Rational Function

Express the following interval in Set notation:
(-7, 15]

• { x | -7 ≤ x ≤ 15 }

• { x | -7 < x ≤ 15 }

• { x | -7 ≤ x < 15 }

• { x | -7 < x < 15 }

Write the following in interval notation
-7 ≤ x < 8

• (-7, 8)

• [-7, 8)

• [-7, 8]

• (-7, 8]

Write the inequality in interval notation.

• (-2,5)

• (-∞,-2) or (5,∞)

• [-2,5]

• (-∞,-2] or [5,∞)

a function that can be written as a ratio of two separate functions.

• Discontinuous Graph

• x-intercept

• Rational Function

• Continuous Graph

the set of all possible x-values.

• Domain

• Range

• Interval Notation

• Piecewise Function

a way of writing subsets of a real number line.

• Domain

• Range

• Interval Notation

• Piecewise Function

Which parent function is this?

• Quadratic

• Cubic

• Linear

• Rational

Answer explanation

The correct answer is 'Rational' because a rational function is defined as the ratio of two polynomials. This distinguishes it from quadratic, cubic, and linear functions, which have different forms and characteristics.

State the DOMAIN in interval notation.

• (-∞,∞)

• [0,∞)

• (-∞,0]

• [-∞,∞]

Answer explanation

The domain of a function is the set of all possible input values. The correct choice, (-∞,∞), indicates that all real numbers are included, meaning any real number can be an input.

What interval notation does the number line graph represent?

• [∞, -5)

• (∞, -5)

• [-5, ∞)

• (-5, ∞)

Answer explanation

The number line graph starts at -5 and includes it (indicated by the bracket) and extends to positive infinity (not included, indicated by the parenthesis). Thus, the correct interval notation is [-5, ∞).

Look at the Graph. Write the inequality in interval notation.

• [-4, -1)

• (-4, -1)

• (-4, -1]

• [-4, -1]

Answer explanation

The interval notation [-4, -1) indicates that -4 is included (closed bracket) and -1 is not included (open bracket). Therefore, the correct choice is [-4, -1).