AP Calculus AB Summer Review Worksheet A

Flashcards covering inequalities, interval notation, domain/range, and function transformations from the AP Calculus AB Summer Review Worksheet A by Poyner and Brooks.

Interval Notation

A mathematical method for writing solution sets of inequalities using symbols such as parentheses $(\text{ or })$ for non-inclusive boundaries and brackets $[\text{ or }]$ for inclusive boundaries.

Absolute Value Inequality $|x - 3| < 4$

The solution set in interval notation is $(-1, 7)$.

Absolute Value Inequality $|x + \text{π}| < \frac{7}{6}\text{π}$

The solution set in interval notation is $(-\frac{13}{6}\text{π}, \frac{1}{6}\text{π})$.

Absolute Value Inequality $\frac{7}{8} \text{≤} |x - 4| \text{≤} 2 \frac{1}{8}$

The solution set in interval notation is $[1 \frac{7}{8}, 3 \frac{1}{8}] \text{∪} [4 \frac{7}{8}, 6 \frac{1}{8}]$.

Function $f(x) = \text{√}{\text{sin}(\frac{\text{π}}{3}x)} + 2$

A function where the domain is listed as $D: (-\text{∞}, 0) \text{∪} (0, \text{∞})$ and the range is $R: [1, \text{√}{3}]$.

Function $g(x) = \frac{\text{√}{x+3}}{x^2-9}$

A function where the domain is listed as $D: (-3, 2] \text{∪} (3, \text{∞})$ and the range is $R: [0, \text{∞})$.

Roots of $p(x) = x^3 - 12x - 11$

The exact values where the function equals zero are $x = -1$ and $x = \frac{1 \text{±} 3\text{√}{5}}{2}$.

Solution set for $p(x) \text{≤} 0$

The interval notation for the set where the function is less than or equal to zero is $(-\text{∞}, \frac{1 - 3\text{√}{5}}{2}] \text{∪} [-1, \frac{1 + 3\text{√}{5}}{2}]$.

Graph Transformation $h(x) = |p(x)|$

The transformation that reflects the portion of the graph of $p(x)$ that lies below the x-axis across the x-axis to become positive.

Graph Transformation $g(x) = p(|x|)$

The transformation that replaces the portion of the graph for $x < 0$ with the reflection of the portion of the graph where $x \text{≥} 0$ across the y-axis.