Polynomial and Rational Functions

It has not shifted but is reflected over the y-axis due to multiplication by -2.

It is shifted right by five and up by seven with reflection across x-axis due to multiplication by -2.

It is shifted left by five and down by seven with no reflection across any axis.

It is shifted right by five and down seven with reflection across y-axis due to multiplication of x-coordinates by -1/5.

v₀=-64 feet per second

v₀=32 feet per second

v₀=96 feet per second

v₀=48 feet per second

The graph becomes steeper and approaches infinity or negative infinity more rapidly.

There will be a vertical stretch by a factor of two in the whole graph.

The x-intercepts of the graph are shifted horizontally.

The end behavior does not change.

The value of a must be less than or equal to zero, while b must be greater than zero.

The value of a must be less than or equal to zero, while b can be either positive or negative.

Both a and b must be positive.

The value of a must be greater than or equal to zero, while b can be negative.

Q evaluates average speed period starting ending points being considered

Q determines acceleration rate corresponding interval

Q measures instantaneous velocity object moving according P's path time T

Q calculates total distance traveled until moment T

One

Zero

The number itself

Negative one

A straight line.

A curve that never touches the x-axis.

An oscillating wave pattern.

A U-shaped curve.

An integer value where the graph crosses the x-axis.

A fraction greater than one where the graph touches but does not cross the x-axis.

A complex number that causes shifts in the vertical asymptote.

A negative decimal point where the graph has a local minimum.

$(x^2 - x)$

$(2x - 3)$

$(x - 1)$

$(x + 4)$

j(x) = (x-6)^3

g(x) = (x + 4)(x - 4)

f(x) = (x - 2)^2 + 3

h(x) = (x +5)(x -5)(x-1)