3-7 Parts 1-2 Alg 2: Even/Odd and Translations

Front

What is an even function?

Back

A function f(x) is even if for every x in the domain, f(-x) = f(x). The graph of an even function is symmetric about the y-axis.

Front

What is an odd function?

Back

A function f(x) is odd if for every x in the domain, f(-x) = -f(x). The graph of an odd function is symmetric about the origin.

Front

What does it mean if a function is neither even nor odd?

Back

A function is neither even nor odd if it does not satisfy the conditions for being even or odd. Its graph does not exhibit symmetry about the y-axis or the origin.

Front

Determine if f(x) = 4x^3 is even, odd, or neither.

Back

f(x) = 4x^3 is an odd function because f(-x) = -4x^3 = -f(x).

Front

What is the general form of a cubic function?

Back

A cubic function can be expressed as f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

How do you determine if a function is even or odd using its graph?

Back

To determine if a function is even, check for y-axis symmetry. To determine if it is odd, check for origin symmetry.

Front

What is the significance of the leading coefficient in a cubic function?

Back

The leading coefficient (the coefficient of x^3) determines the end behavior of the cubic function's graph.

Front

What is a translation in the context of functions?

Back

A translation is a shift of a graph in the coordinate plane. It can be vertical (up or down) or horizontal (left or right).

Front

How does the equation f(x) = (x - 1)^3 + 4 translate the graph of f(x) = x^3?

Back

The graph of f(x) = (x - 1)^3 + 4 is translated 1 unit to the right and 4 units up from the graph of f(x) = x^3.

Front

What is the effect of a negative leading coefficient in a cubic function?

Back

A negative leading coefficient in a cubic function causes the graph to decrease from left to right.