Absolute Value

Front

What is absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is y = |x|.

Front

How does the graph of y = |x| look?

Back

The graph of y = |x| is a V-shaped graph that opens upwards with its vertex at the origin (0,0).

Front

What effect does adding a constant inside the absolute value have?

Back

Adding a constant inside the absolute value function, like y = |x + c|, shifts the graph horizontally. If c is positive, it shifts left; if negative, it shifts right.

Front

What effect does adding a constant outside the absolute value have?

Back

Adding a constant outside the absolute value function, like y = |x| + c, shifts the graph vertically. If c is positive, it shifts up; if negative, it shifts down.

Front

What is the vertex of the function y = |x - 3| + 2?

Back

The vertex of the function y = |x - 3| + 2 is (3, 2).

Front

How do you find the vertex of y = -|x| + 4?

Back

The vertex of y = -|x| + 4 is at (0, 4). The negative sign indicates the graph opens downwards.

Front

What transformation occurs in y = |x + 1| - 3?

Back

The graph of y = |x + 1| - 3 shifts left 1 unit and down 3 units from the parent function.

Front

What is the equation of the graph that has a vertex at (-2, -7)?

Back

The equation of the graph is y = |x + 2| - 7.

Front

What does the expression |x| = a represent?

Back

The expression |x| = a represents two equations: x = a and x = -a, where a is a non-negative number.