Graph Transformations and Dilation Effects

The video tutorial explains how to perform transformations on graphs in a plane by manipulating equations. It covers vertical and horizontal translations, reflections through the x-axis, and dilations. Each transformation is demonstrated with examples, showing how to shift, reflect, or change the width of graphs, including parabolas and lines. The tutorial emphasizes using graphing calculators to visualize these changes quickly.

What is the primary purpose of transformations in a plane?

• To change the color of the graph

• To manipulate the graph's position and shape

• To add more variables to the equation

• To simplify the equation

How does adding a constant to a function affect its graph?

• It shifts the graph to the left

• It shifts the graph to the right

• It shifts the graph upwards

• It shifts the graph downwards

What happens to the graph of y = 3x^2 if you subtract 3 from it?

• The graph shifts up by 3 units

• The graph shifts left by 3 units

• The graph shifts right by 3 units

• The graph shifts down by 3 units

In horizontal translations, where is the change made in the function?

• At the beginning of the function

• At the end of the function

• Inside the function

• Outside the function

What effect does replacing x with (x - 4) have on the graph?

• Shifts the graph left by 4 units

• Shifts the graph down by 4 units

• Shifts the graph up by 4 units

• Shifts the graph right by 4 units

How does reflecting a parabola through the x-axis affect its appearance?

• It becomes wider

• It becomes narrower

• It flips upside down

• It shifts to the right

What is the result of multiplying a function by -1?

• The graph shifts down

• The graph becomes steeper

• The graph reflects through the x-axis

• The graph shifts up

What does a dilation do to a parabola when multiplied by a constant greater than 1?

• Shifts it down

• Makes it thinner

• Makes it wider

• Shifts it up

If a line becomes less steep, what transformation has likely occurred?

• Reflection

• Dilation

• Horizontal translation

• Vertical translation

What happens to a graph when the absolute value of a dilation constant is between 0 and 1?

• The graph becomes wider

• The graph becomes steeper

• The graph shifts right

• The graph shifts left