Exploring Absolute Value Transformations

This video tutorial explains transformations on absolute value graphs using the function f(x) = a|x-h|+k. It covers how the variables a, h, and k affect the graph. Adjusting k results in vertical shifts, while h causes horizontal shifts. The variable a influences the graph's stretch and reflection. The video also explains how to determine the vertex of the graph using the values of h and k.

What is the general form of the absolute value function discussed in the video?

• f(x) = a|x - h| + k

• f(x) = a|x - h| - k

• f(x) = a|x + h| - k

• f(x) = a|x + h| + k

What happens to the graph when the k value is increased?

• It shifts vertically upwards.

• It shifts horizontally to the left.

• It shifts horizontally to the right.

• It shifts vertically downwards.

If the k value is set to -4, what happens to the graph?

• It shifts 4 units to the left.

• It shifts 4 units upwards.

• It shifts 4 units downwards.

• It shifts 4 units to the right.

How does the graph change when the h value is set to 2?

• It shifts 2 units to the left.

• It shifts 2 units downwards.

• It shifts 2 units upwards.

• It shifts 2 units to the right.

What is the effect of setting the h value to -3?

• The graph shifts 3 units to the right.

• The graph shifts 3 units upwards.

• The graph shifts 3 units to the left.

• The graph shifts 3 units downwards.

What happens to the graph when the a value is negative?

• The graph remains unchanged.

• The graph opens downwards.

• The graph opens upwards.

• The graph shifts horizontally.

How does the graph change when the a value is positive?

• The graph opens upwards.

• The graph opens downwards.

• The graph shifts horizontally.

• The graph remains unchanged.

What is the vertex of the absolute value graph when h = 2 and k = 3?

• (3, 2)

• (2, 0)

• (2, 3)

• (0, 0)

Where is the vertex located if both h and k are set to zero?

• (1, 1)

• (1, 0)

• (0, 0)

• (0, 1)

How can you determine the vertex of the graph from the equation?

• By identifying the values of h and k.

• By looking at the coefficient of x.

• By calculating the slope.

• By finding the y-intercept.