Math 4 Unit 2 Piecewise Functions-Flashcard -2B Makeup

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?

Back

To evaluate a piecewise function, identify the interval in which the input value falls and use the corresponding expression to find the output.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at a certain point if there is no output value for that input, often due to division by zero or taking the square root of a negative number.

Front

What is the significance of finding h(x) = 0?

Back

Finding h(x) = 0 helps identify the x-intercepts of the function, which are the points where the graph crosses the x-axis.

Front

How do you find the x-value from a graph when f(x) = k?

Back

To find the x-value when f(x) = k, locate the horizontal line y = k on the graph and determine where it intersects the function.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values (y-values) that the function can produce.

Front

How do you determine continuity in piecewise functions?

Back

A piecewise function is continuous if there are no breaks, jumps, or holes in the graph at the points where the pieces connect.

Front

What is a function's output when x = 2 in a piecewise function defined as: f(x) = { x^2 if x < 2; 3x - 1 if x >= 2 }?

Back

The output is 3 because when x = 2, we use the second piece: f(2) = 3(2) - 1 = 5.

Front

What is the formula for a linear piece in a piecewise function?

Back

A linear piece in a piecewise function can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.