Unit 2 Absolute Value graphing Review

Front

What is the definition of 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 does the graph of y = |x| look like?

Back

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

Front

How does the graph of y = |x - h| shift compared to y = |x|?

Back

The graph shifts horizontally to the right by h units if h is positive and to the left by h units if h is negative.

Front

What effect does a negative sign in front of the absolute value have on the graph?

Back

A negative sign reflects the graph of the absolute value function across the x-axis.

Front

What does the equation y = |x| + k represent?

Back

The equation represents a vertical shift of the graph of y = |x| by k units. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the transformation represented by y = |x + 3| - 2?

Back

The graph shifts left 3 units and down 2 units.

Front

How do you determine the vertex of the graph of y = a|x - h| + k?

Back

The vertex is at the point (h, k).

Front

What is the effect of changing the value of 'a' in the equation y = a|x - h| + k?

Back

Changing 'a' affects the vertical stretch or compression of the graph. If |a| > 1, the graph stretches; if 0 < |a| < 1, it compresses.

Front

What is the equation of the graph that opens downwards and has a vertex at (2, 4)?

Back

The equation is y = -|x - 2| + 4.

Front

What does the term 'transformation' refer to in graphing?

Back

Transformation refers to changes made to the graph of a function, including shifts, reflections, stretches, and compressions.