Alg 2 Test 8 - Absolute Value Transformations

Front

What does the 'a' in the equation y = a|x-h| + k represent?

Back

The 'a' represents the vertical stretch or compression and the direction of the opening of the absolute value graph. If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards.

Front

What transformation occurs when 'a' is greater than 1 in the equation y = a|x-h| + k?

Back

The graph is vertically stretched, making it narrower.

Front

What transformation occurs when '0 < a < 1' in the equation y = a|x-h| + k?

Back

The graph is vertically compressed, making it wider.

Front

What does the 'h' in the equation y = a|x-h| + k represent?

Back

The 'h' represents the horizontal shift of the graph. If 'h' is positive, the graph shifts to the right; if 'h' is negative, it shifts to the left.

Front

What does the 'k' in the equation y = a|x-h| + k represent?

Back

The 'k' represents the vertical shift of the graph. If 'k' is positive, the graph shifts up; if 'k' is negative, it shifts down.

Front

What is the vertex of the absolute value function y = a|x-h| + k?

Back

The vertex is the point (h, k), which is the highest or lowest point of the graph depending on the value of 'a'.

Front

How does the graph of y = |x| compare to y = a|x|?

Back

The graph of y = a|x| is a vertical stretch or compression of the graph of y = |x|, depending on the value of 'a'.

Front

What happens to the graph of y = |x| when it is transformed to y = |x| + k?

Back

The graph shifts vertically by 'k' units. If 'k' is positive, it shifts up; if 'k' is negative, it shifts down.

Front

What happens to the graph of y = |x| when it is transformed to y = |x-h|?

Back

The graph shifts horizontally by 'h' units. If 'h' is positive, it shifts to the right; if 'h' is negative, it shifts to the left.

Front

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

Back

The graph opens downwards, and the vertex is the highest point of the graph.