1A Piecewise and Absolute Value Function

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 translate a function horizontally?

Back

To translate a function horizontally, you add or subtract a value from the input variable (x). For example, f(x + c) shifts the graph left by c units, while f(x - c) shifts it right by c units.

Front

How do you translate a function vertically?

Back

To translate a function vertically, you add or subtract a value from the output of the function. For example, f(x) + c shifts the graph up by c units, while f(x) - c shifts it down by c units.

Front

What does the absolute value function represent?

Back

The absolute value function represents the distance of a number from zero on the number line, regardless of direction.

Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is f(x) = |x - h| + k, where (h, k) is the vertex of the V-shaped graph.

Front

What is the vertex of the function f(x) = |x + 4| - 9?

Back

The vertex of the function f(x) = |x + 4| - 9 is (-4, -9).

Front

How do you find the value of f(0) for f(x) = |x + 4| - 9?

Back

To find f(0), substitute 0 for x: f(0) = |0 + 4| - 9 = |4| - 9 = 4 - 9 = -5.

Front

What is the effect of the '+ k' in the absolute value function?

Back

The '+ k' in the absolute value function shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the effect of the '- h' in the absolute value function?

Back

The '- h' in the absolute value function shifts the graph horizontally. If h is positive, the graph shifts left; if h is negative, it shifts right.

Front

How do you determine the total distance covered in a piecewise function?

Back

To determine the total distance covered in a piecewise function, calculate the distance for each segment of the function and sum them up.