Exponential and Logarithmic Functions

r(x)'s behavior cannot be determined without further information about p and q

$r(x)$ has a jump discontinuity at $x=a$

$r(x)$ is continuous everywhere including at $x=a$

$r(x)$ has an infinite discontinuity at $x=a$

$\int_{0}^{\text{time of } v(t) - r(t)} dt$

Quadratic Height

Height over Time

Double Height

F(x) is less than g(x) for all values in their domains

Functions are equal within the specified domain

Inequality

Intersection points

Incorrect reflectional symmetry about the origin.

Incorrect rotational symmetry around its vertex.

Incorrect no symmetry because it passes through both quadrants I and II.

Even symmetry about the y-axis.

Using synthetic division to simplify terms without considering inequalities.

Graphical interpretation on a coordinate plane.

Solving as though it were only a quadratic equation.

Applying long division disregarding whether terms are linear or quadratic.

A straight line passing through point c without changing direction.

An enclosed area under the curve near point c due to a local minimum or maximum.

A tangent line touching only once at point c but nowhere else on the graph nearby it.

A jump between two points with no connection line on either side of c.

A straight line with a negative slope passing through the origin.

A downward-opening parabola crossing the y-axis at -1.

A sine wave starting at $y=-\frac{\pi}{2}$ and going indefinitely in both directions.

A parabola opening upwards with vertex at (0,0)

$g'(x) > 0$ for all $x$ in its domain.

The sign of $g'(x)$ depends on the value of $x$.

$g'(x) < 0$ for all $x$ in its domain.

$g'(x)$ does not exist for any $x$ in its domain.

Growth without bound

Approaching a horizontal asymptote

Oscillating between finite limits

Decreasing towards a loop

A constant cost across all production volumes leading to uniform revenue increase.

Maximum production capacity reached leading to steady revenues despite increased prices.

Situations where products cannot be sold result in undefined prices-revenue points.

A linear increase in demand results in proportional increases in revenue as price rises.