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 the input variable.

Front

What is the parent function of y = |x|?

Back

The parent function of y = |x| is the absolute value function, which outputs the non-negative value of x.

Front

Describe the transformation of the function y = |x + 2| - 5 from the parent function y = |x|.

Back

The function is translated left 2 units and down 5 units.

Front

What does a vertical shrink of ⅔ mean in a function?

Back

A vertical shrink of ⅔ means that the output values of the function are multiplied by ⅔, making the graph flatter.

Front

How do you express the function 5|x-2|-3 as a piecewise function?

Back

5|x-2|-3 can be expressed as: 5x-13 for x >= 2 and -5x+7 for x < 2.

Front

What is the effect of a horizontal shift to the right in a function?

Back

A horizontal shift to the right means that the input values of the function are increased by a certain amount.

Front

Evaluate f(-4) if f(x) is defined piecewise as: f(x) = { 7 if x < 0; -x + 3 if x >= 0 }

Back

f(-4) = 7.

Front

What does the notation f(x) = ⅔(x - 7)² indicate about the transformations of the parent function?

Back

It indicates a vertical shrink by a factor of ⅔ and a horizontal shift to the right by 7 units.

Front

How do you determine the output of a piecewise function?

Back

To determine the output, identify which interval the input value falls into and use the corresponding expression.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, indicating the maximum or minimum value of the function.