Unit 1B Test Review

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32 Terms

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Constant Function

f(x) = c

<p>f(x) = c</p>
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Linear Function

f(x) = x

<p>f(x) = x</p>
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Quadratic (Square) Function

f(x) = x²

<p>f(x) = x<span>²</span></p>
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Cubic Function

f(x) = x³

<p>f(x) = x³</p>
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Square Root Function

f(x) = √x

<p>f(x) = <span style="font-size: medium">√x</span></p>
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Cube Root Function

f(x) = ∛x

<p>f(x) = ∛x</p>
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Absolute Value Function

f(x) = |x|

<p>f(x) = |x|</p>
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Reciprocal Function

f(x) = 1/x

<p>f(x) = 1/x</p>
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Absolute Maximum

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

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Absolute Minimum

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

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Local Maximum

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

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Local Minimum

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

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X-intercept(s)

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

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Y-intercept

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

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Interval of Increase

Where the function values are rising as x moves rightward.

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Interval of Decrease

Where the function values are falling as x moves rightward.

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Constant Interval

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

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Even Function

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

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Odd Function

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

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How can you tell if a function is even?

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

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How can you tell if a function is odd?

Visualize rotating the graph 180 degrees around the origin.

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Which parent functions are even?

Constant, quadratic, absolute value function (CAQ)

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Which parent functions are odd?

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

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Which parent function is neither odd or even?

Square root function

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

All except reciprocal and constant function

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

All except square and reciprocal

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

Linear, cubic, and cube root functions (LCC)

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

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

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

Quadratic (squared) and absolute value function

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

Square and reciprocal

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