Domain: The domain \((-\infty , \infty )\).

Zeros: Core Exponential Functions have no zeros.

Continuity: Core Exponential Functions are continuous.

End-Behavior:

If \(r > 1\), the Core Exponential Functions tend to \(0\) as the domain becomes unbounded negatively. Core Exponential Functions tend to \(\infty \) as the domain becomes unbounded positively.

If \(0 < r < 1\), then this is reversed.

Behavior (Inc/Dec):

If \(r > 1\), then Core Exponential Functions are increasing functions.

If \(0 < r < 1\), then Core Exponential Functions are decreasing functions.

Global Maximum and Minimum: Core Exponential Functions have no global maximum or minimum.

Local Maximum and Minimum: Core Exponential Functions have no local maximums or minimums.

Range: The range of a Core Exponential Function is either \((0,\infty )\) or \((-\infty , 0)\).

Domain: The domain \((0, \infty )\).

Zeros: Core Logarithmic Function have \(1\) as their only zero.

Continuity: Core Logarithmic Functions are continuous.

End-Behavior: Since the domain is \((0, \infty )\), Core Logarithmic Functions only end-behavior as the domain become unbounded positively.

If \(r > 1\), then

The other side is called Singularity Behavior.

If \(0 < r < 1\), then

The other side is called Singularity Behavior.

Behavior (Inc/Dec):

If \(r > 1\), then Core Logarithmic Functions are increasing functions.

If \(0 < r < 1\), then Core Logarithmic Functions are decreasing functions.

Global Maximum and Minimum: Core Logarithmic Functions have no global maximum or minimum.

Local Maximum and Minimum: Core Logarithmic Functions have no local maximums or minimums.

Range: The range of Core Logarithmic Functions is \((-\infty ,\infty )\).

Domain: The domain both functions is \((-\infty , \infty )\).

Zeros: Both functions have zeros and since both functions are periodic, they have an infinite number of zeros.

• Zeros of \(\sin (x)\) are \(k \pi \, | \, k \in \mathbb {Z}\).
• Zeros of \(\cos (x)\) are \(\frac {\pi }{2} + k \pi \, | \, k \in \mathbb {Z}\).

Continuity: Both functions are continuous.

End-Behavior: Both functions continue to oscillate.

Behavior (Inc/Dec): Both functions switch back-and-forth between increasing and decreasing with a period of \(2\pi \).

• \(\sin (x)\) increases on \(\left (0, \frac {\pi }{2} \right )\)
• \(\sin (x)\) decreases on \(\left (\frac {\pi }{2}, \frac {3\pi }{2} \right )\)
• \(\sin (x)\) increases on \(\left (\frac {3\pi }{2}, 2\pi \right )\)

• \(\cos (x)\) decreases on \((0, \pi )\)
• \(\cos (x)\) increases on \((\pi . 2\pi )\)

Global Maximum and Minimum: Both functions have a global maximum of \(1\) and a global minimum of \(-1\).

Local Maximum and Minimum: Both functions \(1\) and \(-1\) as their local extrema.

Range: The range of both functions is \([-1, 1]\).

Domain: The domain is \((-\infty , \infty )\).

Zeros: \(0\) is the only zero.

Continuity: The Core Absolute Value Function is continuous.

End-Behavior: The Core Absolute Value Function becomes unbounded positively on both sides.

Behavior (Inc/Dec):

The Core Absolute Value Function decreases on \((-\infty , 0)\) and increases on \((0, \infty )\)

Global Maximum and Minimum: The Core Absolute Value Function has \(0\) as its global minimum and it has no global maximum.

Local Maximum and Minimum: The Core Absolute Value Function has \(0\) as its only local minimum and it has no local maximum.

Range: The range is \([0, \infty )\).