Pre-Calc 12 Basic Functions

Linear

f(x)=x

Linear Domain

(−∞, ∞)

Linear Range

(−∞, ∞)

Linear Extrema

None

Linear Symmetry

odd

Linear End Behavior

−∞ and ∞

Linear Others

Continuous, Unbounded and No VA or HA

Quadratic

f(x)=x²

Quadratic Domain

(−∞, ∞)

Quadratic Range

[0, ∞)

Quadratic Extrema

Minimum of 0 when x=0

Quadratic Symmetry

Even

Quadratic End Beahvior

lim f(x)= ∞ , x = + - ∞

Quadratic Others

Continuous Bounded below and No VA or HA

Cubic

f(x)=x³

Cubic Domain

(−∞, ∞)

Cubic Range

(−∞, ∞)

Cubic Extrema

None

Cubic Symmetry

Odd

Cubic End Behavior

−∞ & ∞

Cubic Others

Continuous, Unbounded, No VA or HA

Reciprocal or Rational

f(x)=1/x

Rational Domain

(−∞, 0)u(0,∞)

Rational Range

(−∞, 0)u(0,∞)

Rational Extrema

None

Rational Symmetry

Odd

Rational End Behavior

lim f(x) = 0 (both) and −∞ ∞

Rational Other

Infinite Discontinuity at x=0, Unbounded, HA y=0 and VA x=0

Square Root

f(x)= √x

Square Root Domain

[0, ∞)

Square Root Range

[0, ∞)

Square Root Extrema

Minimum of 0 when x=0

Square Root Symmetry

Neither

Square Root End Behavior

DNE infinite and infinite infinite

Square Root Others

Conitnuous Bounded below NO VA HA

Absolute Value

f(x)=|x|

Absolute Value Domain

(−∞, ∞)

Absolute Value Range

[0, ∞)

Absolute Value Extrema

Minimum of 0 when x=0

Absolute Value Symmetry

Even

Absolute Value End Behavior

Infinite and +- infinite

Absolute Value Others

Continuous bounded below NO VA HA

Growth

f(x)=e^x

Growth and Decay Domain

(−∞, ∞)

Growth and Decay Range

(0, ∞)

Growth and Decay Extrema

None

Growth and Decay Symmetry

Neither

Growth and Decay Others

Continuous Bounded Below HA y=0 No VA

Decay

f(x)= e^-x

Growth End Behavior

0 and -infinity and infinity and infinity

Decay End Behavior

infinite negative infinite and 0 infinity

Sine

f(x)= sin x

Cosine

f(x) = cos x

Sine and Cosine Domain

(−∞, ∞)

Sine and Cosine Range

[-1,1]

Sine and Cosine Extrema

Infinite Extrema, Max at 1 and Min at -1

Sine and Cosine End Behavior

DNE +- infinite

Sine ane Cosine others

Coninuous bounded and No VA HA

Sine Symmetry

Odd

Cosine Symmetry

Even

Greatest Interger

f(x)= int (x)

Greatest Integer Domain

(−∞, ∞)

Greatest Integer Range

all integers

Greatest Integer Extrema

None

Greatest Integer Extrema

Neither

Greatest Integer

-infinity postive infinity

Greatest Integer other

Jump discontinuity unbounded No VA HA

Logarithmic

f(x)= ln x

Logarithmic Domain

(0, ∞)

Logarithmic Range

(−∞, ∞)

Logarithmic Extrema

None

Logarithmic Symmetry

Neither

Logarithmic End Behavior

DNE -infinity and infinity infinity

Logarithmic others

Continuous unbounded No HA VA x=0

Logistic

f(x)= 1/1+e^-x

Logistic Domain

(−∞, ∞)

Logistic Range

(0,1)

Logistic Extrema

None

Logistic Symmetry

Neither

Logistic End Behavior

0 −∞ and 1 ∞

Logistic others

Continuous Bounded No VA HA y=0 y=1