Evaluating Piecewise Functions

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different intervals of its domain.

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which interval the point falls into and then use the corresponding expression to find the function's value.

Front

What does it mean if a piecewise function is undefined at a certain point?

Back

If a piecewise function is undefined at a certain point, it means that there is no corresponding output value for that input in the function's definition.

Front

Evaluate f(0) if f(x) = { 4, x < 1; 2x, x >= 1 }

Back

f(0) = 4.

Front

Evaluate h(5) if h(x) = { x^2 - 10, x < 0; 2x + 2, x >= 0 }

Back

h(5) = 12.

Front

What is the significance of the domain in piecewise functions?

Back

The domain of a piecewise function specifies the intervals for which each piece of the function is valid.

Front

Evaluate f(4) if f(x) is defined graphically and f(4) is marked as -1.

Back

f(4) = -1.

Front

Evaluate f(-10) if f(x) is defined graphically and f(-10) is marked as -10.

Back

f(-10) = -10.

Front

Evaluate g(-2) if g(x) = { 3x + 1, x < -1; -x + 5, x >= -1 }

Back

g(-2) = 7.

Front

What is the output of a piecewise function if the input is outside its defined intervals?

Back

The output is undefined if the input is outside the defined intervals of the piecewise function.