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 use the corresponding expression to find the function's value.

Front

What is the value of g(-2) if g(x) is defined as follows: g(x) = { 7 if x < -1, -1 if -1 ≤ x < 0, 1 if x ≥ 0 }?

Back

g(-2) = 7.

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

How do you find the total cost in a piecewise function scenario?

Back

To find the total cost in a piecewise function scenario, calculate the cost for each segment of the function based on the defined rates and sum them up.

Front

Evaluate f(2) if f(x) = { 0 if x < 1, 1 if 1 ≤ x < 3, 3 if x ≥ 3 }.

Back

f(2) = 1.

Front

What is the total earnings for a painter who charges $12/hour for the first 40 hours, $18/hour for the next 10 hours, and $24/hour thereafter for a 70-hour week?

Back

Total earnings = $1140.

Front

What is the significance of the domain in piecewise functions?

Back

The domain in piecewise functions specifies the intervals for which each piece of the function is applicable.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval, ensuring to use open or closed circles to indicate whether endpoints are included.

Front

What is the value of g(-6) if g(x) is defined as follows: g(x) = { 4 if x < -5, -1 if -5 ≤ x < 0, 7 if x ≥ 0 }?

Back

g(-6) = 4.