Algebra 1 Common Core Student Edition, Grade 8-9

You can think of functions whose graphs have similar features as families of functions.

You have studied six families of functions in this book. Their properties and graphs are

shown in the summary.

Co n c ep t Su m m a r y Families of Functions

Li n ear f u n ct i o n Qu ad r at i c f u n ct i o n

y = ax2 + bx + c

parent function: f{x) = x

slope = m

y-intercept = b

The greatest exponent is 1.

Absolute value function

parent function: /(x) = |x|

Shift y = ]x| horizontally a units.

Shift y = \x\ vertically b units,

vertex at (a, b)

The greatest exponent is 1.

Sq u a r e r o o t f u n c t i o n

y = Vx — h + c

Shift y = Vx horizontally b units.

Shift y = V x vertically c units.

The variable is under the radical.

parent function: /(x) = x2

parabola with axis of

symmetry at x =

The greatest exponent is 2.

Ex p o n e n t i a l f u n c t i o n

growth where b > 1

decay where 0 < b < 1

The variable is the exponent.

Rat i o n al f u n ct i o n

' x - b + c

vertical asymptote at x = b

horizontal asymptote at y = c

The variable is in the denominator.

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