4A Even, Odd, Neither Functions 3 24 25

Front

What is an even function?

Back

A function f(x) is even if f(-x) = f(x) for all x in the domain of f. 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 f(-x) = -f(x) for all x in the domain of f. 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

Identify the type of function: g(x) = x^4 + x^2

Back

Even function, because g(-x) = (-x)^4 + (-x)^2 = x^4 + x^2 = g(x).

Front

What is the transformation represented by f(x + 5) + 3?

Back

This transformation shifts the graph of f(x) 5 units to the left and 3 units up.

Front

What is the equation of the red parabola if it is given as g(x) = (x + 6)^2 - 4?

Back

The equation of the red parabola is g(x) = (x + 6)^2 - 4.

Front

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

Back

A function is even if the left side of the graph mirrors the right side about the y-axis. It is odd if the graph rotates 180 degrees around the origin.

Front

What is the parent function of g(x) = |x|?

Back

The parent function is f(x) = |x|, which is the absolute value function.

Front

What does the transformation g(x) = |x - 2| represent?

Back

This transformation shifts the graph of the parent function f(x) = |x| 2 units to the right.

Front

What is the significance of a solid dot on a graph?

Back

A solid dot indicates that the point is included in the function's domain, meaning the function value is defined at that point.