Even, Odd, Neither

Front

What is an even function?

Back

A function f(x) is called even if f(-x) = f(x) for all x in the domain of f. Graphically, even functions are symmetric about the y-axis.

Front

What is an odd function?

Back

A function f(x) is called odd if f(-x) = -f(x) for all x in the domain of f. Graphically, odd functions are 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. This means that f(-x) is not equal to f(x) or -f(x).

Front

Give an example of an even function.

Back

f(x) = x^2 is an example of an even function because f(-x) = (-x)^2 = x^2.

Front

Give an example of an odd function.

Back

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

Front

What is the range of the function f(x) = x^2?

Back

The range of f(x) = x^2 is [0, ∞) because the output is always non-negative.

Front

What is the range of the function f(x) = x^3?

Back

The range of f(x) = x^3 is all real numbers (-∞, ∞) because it can take any value.

Front

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

Back

If the graph is symmetric about the y-axis, it is even. If it is symmetric about the origin, it is odd.

Front

What is the significance of the y-intercept in determining function properties?

Back

The y-intercept can help identify if a function is even or odd; even functions have y-intercepts at (0, f(0)) and odd functions pass through the origin.

Front

When is the velocity of a function decreasing?

Back

Velocity is decreasing when the derivative of the function is negative.