Polynomial and Rational Functions

$x^2-49$

$-49+x^2$

$x^z+14+49$

$49-x^z$

$x+8$

$x-8$

$x+z$

$x*8$

7y^4

7y^3

12y^4

12y^3

Meters or feet

Liters or gallons

Kilograms or pounds

Degrees or radians

100

10

0

-10

They both contain the same number of terms after simplification.

They yield the same value for all values within their domains.

They result in functions whose graphs intersect at some point.

They have identical coefficients for all corresponding terms.

Jump discontinuity

Infinite discontinuity

No discontinuity

Point discontinuity

x > 6

x > 5

x < 4

x < 3

-6

-2

Horizontal stretch by factor $\times -0.5$, reflect over x-axis, vertical shrink by multiple $\times -6$ then down five units.

Reflect over x-axis, vertical stretch by factor of $-5$, horizontal shrink by multiple of $-0.5$, shift left by six units.

Horizontal shrink factor fold, vertical stretch unit, shift left half-by-half then down eight units.

Reflect over y-axis, vertical stretch by factor $\times 8$, shift right multiple $\times -0.5$ then up $\times 6$ units.