Absolute Value Graph Transformations

Front

What is the effect of adding a constant to the absolute value function?

Back

Adding a constant (k) to the absolute value function y = |x| shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What does the equation y = |x - h| represent in terms of horizontal shifts?

Back

The equation y = |x - h| shifts the graph horizontally. If h is positive, the graph shifts right; if h is negative, it shifts left.

Front

How does the equation y = |x + 4| + 2 transform the graph of y = |x|?

Back

The graph of y = |x| is shifted left 4 units and up 2 units.

Front

What is the transformation of the graph for y = |x - 5| - 3?

Back

The graph of y = |x| is shifted right 5 units and down 3 units.

Front

What does the term 'absolute value' signify in mathematics?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

Front

How does the graph of y = |x| change when the coefficient of x is negative, as in y = |-x|?

Back

The graph remains the same because the absolute value negates the effect of the negative sign, resulting in y = |x|.

Front

What is the general form of an absolute value function?

Back

The general form is y = a|bx - h| + k, where (h, k) is the vertex, 'a' affects the vertical stretch/compression, and 'b' affects the horizontal stretch/compression.

Front

What happens to the graph of y = |x| when the coefficient 'a' is negative?

Back

If 'a' is negative, the graph reflects over the x-axis, but since it's an absolute value function, it will still open upwards.

Front

How do you determine the vertex of the absolute value function y = |x - 3| + 2?

Back

The vertex is at the point (3, 2), which is derived from the transformations applied to the basic function y = |x|.

Front

What is the significance of the vertex in the graph of an absolute value function?

Back

The vertex is the point where the graph changes direction and represents the minimum (or maximum, if reflected) value of the function.