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 $y=2$.

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 $x=c$.

Vertical tangents would appear for all values except where $(x-3)^2 >0$.

Vertical tangents would never appear as $(x-3)^2 >0$ for all real numbers except at x equals three ($x \neq 3$).

Vertical tangents would appear where y equals three ($y=3$).

Vertical tangents would appear where x equals three ($x=3$).

Uniformly negative slopes throughout the entire field.

Horizontal tangents at points where $\cos(x) = 0$.

Slopes that become less steep as both variables increase.

Diagonal lines pointing downwards from left to right across all quadrants.

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

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

-1

$x^2$

0

1

The function is undefined at that point

The function is increasing at that point

The function is constant at that point

The function is decreasing at that point

The behavior of the function near critical points

The average rate of change of the function

The antiderivative of the function

The area under the function's graph