Absolute Value Graphs and Transformations

The video tutorial explains the general form of absolute value graphs, focusing on the role of variables H and K in controlling horizontal and vertical movements. The main focus is on the variable 'a', which affects the slope and width of the graph. Through examples, the tutorial demonstrates how different values of 'a' compress or widen the graph and how division affects the slope. The tutorial concludes by combining vertex movement with the 'a' multiplier, showing how negative values of 'a' invert the graph.

What do the variables H and K represent in the general form of absolute value graphs?

• H controls the slope, K controls the vertex position.

• H controls left and right movements, K controls up and down movements.

• H and K both control the slope.

• H controls up and down movements, K controls left and right movements.

What is the effect of a number multiplied outside the absolute value on the graph?

• It has no effect on the graph.

• It changes the graph's color.

• It changes the vertex position.

• It affects the slope of the graph.

What is the general effect of a positive multiplier on the graph's slope?

• It shifts the graph downwards.

• It shifts the graph upwards.

• It makes the graph narrower.

• It makes the graph wider.

What is the effect of a positive multiplier greater than 1 on the graph's slope?

• It shifts the graph downwards.

• It shifts the graph upwards.

• It makes the graph wider.

• It makes the graph narrower.

What is the effect of a positive multiplier on the graph's vertex position?

• It shifts the vertex upwards.

• It shifts the vertex to the left.

• It shifts the vertex to the right.

• It does not affect the vertex position.

What is the effect of a positive multiplier on the graph's direction?

• It inverts the graph.

• It does not affect the graph's direction.

• It shifts the graph to the left.

• It shifts the graph to the right.

In the example of 3 times the absolute value of x, what is the first step in graphing?

• Calculate the y-intercept.

• Draw the axis.

• Determine the slope.

• Find the vertex position.

How does the graph of 3|x| differ from the basic |x| graph?

• It is wider.

• It is shifted to the right.

• It is shifted upwards.

• It is narrower.

What is the vertex position for the graph of 3|x|?

• (0, 0)

• (1, 1)

• (-1, -1)

• (0, 1)

What is the slope of the rays when a is 3 in the graph of 3|x|?

• 2

• 1

• 3

• 1/3