Effects of Absolute Value Graphs

The video tutorial explains how to draw and interpret absolute value graphs, focusing on horizontal shifts. It demonstrates how to combine graphs by adding them together and analyzing the resulting gradients. Using a water analogy, the tutorial illustrates how graph behavior changes when combining efforts. The conclusion provides an algebraic explanation of the final graph shape.

What is the effect of a horizontal shift on an absolute value graph?

• It reflects the graph over the x-axis.

• It changes the slope of the graph.

• It moves the graph up or down.

• It moves the graph left or right.

How does adding a positive constant inside the absolute value function affect its graph?

• It shifts the graph to the left.

• It makes the graph steeper.

• It shifts the graph to the right.

• It reflects the graph over the y-axis.

When combining two absolute value graphs, what happens to the gradient if both have a gradient of 1?

• The gradient becomes -1.

• The gradient becomes 1.

• The gradient becomes 2.

• The gradient becomes 0.

What analogy is used to describe the effect of combining two increasing graphs?

• Two people pulling a rope.

• Two people pouring water into a bath.

• Two people climbing a hill.

• Two people pushing a car.

What happens to the graph when both functions are decreasing?

• The graph remains unchanged.

• The graph becomes shallower.

• The graph becomes steeper.

• The graph becomes horizontal.

In the context of the graph, what does it mean when one function is increasing and the other is decreasing?

• The graph becomes horizontal.

• The graph becomes steeper.

• The graph becomes a circle.

• The graph becomes a parabola.

What is the final shape of the combined graph when the effects of both functions cancel each other out?

• A curved line.

• A diagonal line.

• A horizontal line.

• A vertical line.

What is the resulting line when the gradients of two functions cancel each other out?

• A vertical line.

• A line with a positive slope.

• A line with a negative slope.

• A horizontal line.

What is the value of the horizontal line in the final graph?

• 5

• 2

• 3

• 4

What happens to the x-values in the final algebraic expression of the combined graph?

• They cancel each other out.

• They are subtracted from each other.

• They are multiplied together.

• They are added together.