Unit 1B Test Review

Constant Function

Constant Function

f(x) = c

Linear Function

f(x) = x

Quadratic (Square) Function

f(x) = x²

Cubic Function

f(x) = x³

Square Root Function

f(x) = √x

Cube Root Function

f(x) = ∛x

Absolute Value Function

f(x) = |x|

Reciprocal Function

f(x) = 1/x

Absolute Maximum

The highest point on the entire graph of a function within its domain.

Absolute Minimum

The lowest point on the graph of a function within its domain.

Local Maximum

A point on the graph where the function has a higher value than at any nearby points.

Local Minimum

A point where the function has a lower value than any nearby points.

X-intercept(s)

Found by setting f(x) = 0. The points where the graph crosses the x-axis (where y=0)

Y-intercept

Found by setting f(x) = 0. The point where the graph crosses the y-axis (where x=0).

Interval of Increase

Where the function values are rising as x moves rightward.

Interval of Decrease

Where the function values are falling as x moves rightward.

Constant Interval

An interval where the function remains the same (flat) and does not increase or decrease

Even Function

Symmetrical across the y-axis; f(-x) = f(x)

Odd Function

Origin Symmetry (rotates 180° around the origin), opposite inputs create opposite outputs; f(−x) = −f(x)

How can you tell if a function is even?

Check if the function is mirrored across the y-axis.

How can you tell if a function is odd?

Visualize rotating the graph 180 degrees around the origin.

Which parent functions are even?

Constant, quadratic, absolute value function (CAQ)

Which parent functions are odd?

Linear, cubic, reciprocal, cube root function (Lccr)

Which parent function is neither odd or even?

Square root function

What parent functions have a point at (0,0)?

All except reciprocal and constant function

What parent functions have a domain that is (-∞,∞)?

All except square and reciprocal

What parent functions have a range that is (-∞,∞)?

Linear, cubic, and cube root functions (LCC)

What parent functions have a range that is [0,∞)?

Square root, quadratic (square), absolute value functions (SAQ)

Which parent functions have both an interval of increase and an interval of decrease?

Quadratic (squared) and absolute value function

Which parent functions have a domain that is NOT (-∞,∞)?

Square and reciprocal