Polynomial and Rational Functions

Use different sets of parentheses for subtraction problems without affecting outcome.

Change numbers from negatives to positives while adding them.

Subtract instead if adding during calculations.

Group numbers differently without changing their sum or product.

Distance doubling from y-axis shifting twice as far away is quadrupled to original positioning.

Doubling the height of the curve points movement directly away from the z-axis equals quadratic increase nearness.

Halving the height of the curve makes the point stationary regardless of horizontal movement taking place, except quadrant switching.

Compressed vertically halves the distance point y-axis moved horizontally four spaces is quintupled.

x = -1

x = 1

x = 0

There is no discontinuity

A horizontal shift

A vertical stretch

A vertical shrink

A reflection across the y-axis

It reflects over the y-axis.

It shifts right by $\\pi/2$.

It stretches vertically.

It shifts left by $\\pi/2$.

The number itself

0

Infinity

1

Each point moves closer to x-axis at a distance that is inversely proportional to $k$.

Each point maintains its distance from both axes but rotates around origin based on $k$'s value.

Each point moves $k$ times farther away from the y-axis if its original position was not on this axis.

Each point stays fixed in its original location because only shapes are affected by horizontal stretches, not functions.

The number itself

Infinity

1

Undefined

k > 0

k = .

k < 0

k = 0

The limit would increase by $k$

None, the limit would remain unchanged

The limit would become undefined

The limit would decrease by $k$