Algebra 2 function toolbox

EQN means equation

Constant function

• no slope

• no increase or decrease

• EQN: y = c (c can only be any real #)

Linear function

• has a constant slope

• has one x - intercept & one y - intercept,

• EQN: y = mx + b (m is slope and b is y - intercept)

Quadratic function

• shape is parabola

• the degree is 2

EQN:

• standard form: y = ax²+bx+c

• vertex: y = a (x-h)² + k

• Factor: y = (x + b) (x + c)

graphical features:

• min or max

• y - intercept (only 1)

• 2 x intercepts

Cubic function

• the degree is 3

• EQN: y = ax³ + bx² + cx + d

Graphical features:

• Min & max

• x-intercept (at most 3)

• y - intercept

Quartic function

• EQN: y = ax⁴ + bx³ + cx² + dx + e

• The degree is 4

Graphical features:

• Min/max

• 4 x - intercepts (at most)

• y - intercept (1)

Absolute value function

• EQN: y = |x|

Graphical features:

• min or max (vertex)

• x - intercept (at most 2)

• y - intercept

Exponential growth

• the function is always increasing

• EQN: y = a (b)^x

• (b > 1)

Graphical features:

• exponential functions have horizontal asymptotes.

• An Asymptotes is a value the function approaches, but doesn’t ever touch

Exponential decay

• EQN: y = a(b)^x

• (0 < b < 1)

• exponential functions have horizontal asymptotes.

logarithmic functions

Graphical features:

• there is a vertical Asymptotes

EQN: y = log_b(x)

rational function

• EQN: y = 1/x

• the variable is the denominator

• has both vertical and horizontal asymptotes

Square root function

• clear starting point

• EQN: y = √x

sine function

• EQN: y = sin(x)

• infinite x - intercepts and infinite max/mins

• ONLY ONE y INTERCEPT