Algebra II Unit 1 Test

lock in diva

What parent function is f(x) = x²?

Quadratic function

What parent function is f(x) = x?

Linear function

What parent function is f(x) = x³?

Cubic function

What parent function is f(x) = b^x?

Exponential function

What parent function is 1/x?

Rational function

What parent function is f(x) = |x|?

Absolute value function

What parent function is f(x) = √x

Square root function.

What is the parent function f(x) = 3√x?

Cubic root function

What is the parent function f(x) = log(x)?

Logarithmic function

What is the parent function f(x) = sin(x) OR cos(x)?

Sinusodial function

In transformations, what is a? which axis does a relate to? Is a “inside” or “outside” of the parent function?

a is the vertical stretch and compress factor, it relates to the y-axis, and multiplies outside the parent function.

What is b? Which axis does b relate to? Is b “inside” or “outside” the parent function?

b is the horizontal stretch and compress factor, b is relative to the x-axis, and b multiples “inside” the parent function.

What is h? Is h “inside” or “outside” of the parent function?

h is the horizontal translation factor, and it adds and subtracts “inside” of the parent function.

What is k? Is k “inside” or “outside” of the parent function?

k is the vertical translation factor, and it adds and subtracts “outside” of the parent function.

When a is greater than 1…

VS by a.

When a is between 1 and 0…

VC by a

When a is negative or equal to 0…

Reflection over the x-axis, and if its negative, VS/VC by that number as if it was positive in addition to the reflection.

When b is greater than 1…

HC by 1/b.

When b is between 1 and 0…

HS by 1/b.

When b is equal to or less than 0…

Reflection over y-axis and if negative, HS/HC by 1/b but as if b is positive in addition to the reflection.

When h is less than zero, _ by h. When h is greater than zero, _ by h.

right, left.

When k is greater than zero, _ by k. When k is less than zero _ by k.

up, down.

included values are shown with…

filled circles and brackets. • [ ]

excluded values are shown with…

open circles and parenthesis. ○ ( )

To combine two intervals, use a…

Union symbol (just a u bro)

infinities and negative infinities are always…

excluded.

the domain of a function is…

the set of valid x-values.

The range of a function is…

the set of valid outputs/y-values.

Which parents have no limitations on their domain/range?

Linear, Cubic, and Cube Root parent functions have no limitations on their domain/range. ((-infinity, +infinity) for both)

What is the limitation on Quadratic functions?

Range cannot include negative numbers (neg x neg = pos).

What is the limitation on Exponential functions?

Range cannot include 0s or negs.

What is the limitation on Absolute Value functions?

Range cannot include negs. (AV is distance)

What is the limitation on Square Root functions?

Neither domain nor range can include negative numbers.

What is the limitation on Rational functions?

No zeros can be included in range or domain. (-infinity, 0) (0, +infinity)

What is the x-intercept?

The coordinates where a graph overlaps the x-axis. (0, x)

What is a y-intercept?

The coordinates where a graph overlaps the y-axis. (0, y)

What is the relative maximum?

A point where the y-value is greater than the y-values on either side.

What is a relative minimum?

A point where the y-value is less than the y-values on either side.

What is an asymptote?

An asymptote is a line that a function approaches but never touches.

What does “Positive” ask for?

The set of x-values above the x-axis.

What does “Negative” ask for?

The set of x-values below the x-axis.

What does “Increasing” ask for?

How y-increases from left to right. (ex. (2,5)u(3,8))

What does “Decreasing” ask for?

How y decreases from left to right. (Ex. (5,3))

What does “Constant” ask for?

The set of x values during a time when the y-value is constant. (Ex. (1,3))