Differential Equations

The function has no real-number solutions.

The function must be undefined along the line $x=y$.

The function may exhibit properties consistent with inverse functions.

The function has discontinuities along the line $x=y$.

The rate of change is negative when $y=2$.

The rate of change is zero when $y=2$.

The rate of change is infinite when $y=2$.

The rate of change is increasing when $y=2$.

The rate of change of the function at each point

The integral of the function over a specific interval

The curvature of the function at each point

The magnitude of the slope at each point

Symmetrical slopes around $x=c$ in the field.

A constant slope throughout the entire field.

A horizontal line of tangents at $x=c$.

Discontinuity or break in the slope field at $x=c$.

The derivative is zero indicating a local maximum, minimum, or point of inflection.

The solution curve has an asymptote at that point.

There is no solution to the differential equation at that point.

The function has an undefined derivative at that point.

Rotational symmetry about the origin

Constant vector lengths throughout the field

Uniformly spacing between vectors across the entire field

Vertical vectors adjacent to the Y-axis without rotation

They represent exponential growth functions where solutions rapidly increase over time.

They illustrate solutions to linear equations where solutions grow steadily over time without bound.

They show quadratic functions where solutions accelerate as they move away from their vertex.

They indicate oscillating solutions typical for trigonometric functions.

The solutions are parallel to the slope field lines

The solutions are the points where the slope field lines intersect

The solutions follow the direction of the slope field lines

The solutions are the points where the slope field is undefined

$\frac{dy}{dx}=x^2-9$

$\frac{dy}{dx}=3$

$\frac{dy}{dx}=e^x$

$\frac{dy}{dx}=x+2$

The slope field provides a visual representation of the solution curve's slope at each point

The slope field represents the antiderivative of the solution curve

The slope field determines the tangent line to the solution curve at each point

The slope field represents the integral of the solution curve