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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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).

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF.IF.A.2

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.