Transformations of Linear Functions Explained

The video tutorial covers transformations of linear function graphs, including translations, reflections, stretches, and shrinks. It explains how to apply these transformations to modify the size, shape, position, or orientation of graphs. The tutorial also demonstrates combining multiple transformations and provides a real-world example involving pricing models.

What is the effect of adding a positive constant to the output of a function?

• Shifts the graph to the left

• Shifts the graph down

• Shifts the graph to the right

• Shifts the graph up

If the function y = f(x) is transformed to y = f(x - 3), what is the effect on the graph?

• Shifts the graph 3 units down

• Shifts the graph 3 units up

• Shifts the graph 3 units to the left

• Shifts the graph 3 units to the right

What does the transformation y = -f(x) do to the graph of y = f(x)?

• Reflects it over the x-axis

• Reflects it over the y-axis

• Shifts it down

• Shifts it up

How does the graph of y = f(-x) compare to the graph of y = f(x)?

• It is reflected over the x-axis

• It is shifted down

• It is shifted up

• It is reflected over the y-axis

What happens to the graph of y = f(x) when it is transformed to y = 2f(x)?

• It is horizontally stretched

• It is horizontally shrunk

• It is vertically stretched

• It is vertically shrunk

If a function y = f(x) is transformed to y = f(2x), what is the effect on the graph?

• It is vertically stretched

• It is vertically shrunk

• It is horizontally shrunk

• It is horizontally stretched

Which transformation is applied when y = f(x) changes to y = f(x) + 5?

• Vertical shift 5 units down

• Horizontal shift 5 units left

• Horizontal shift 5 units right

• Vertical shift 5 units up

What is the combined effect of the transformations y = -2f(x) + 3?

• Reflect over y-axis, shrink vertically by 2, shift down by 3

• Reflect over x-axis, shrink vertically by 2, shift down by 3

• Reflect over y-axis, stretch vertically by 2, shift up by 3

• Reflect over x-axis, stretch vertically by 2, shift up by 3

In the cable company example, what is the effect of reducing the monthly fee to $30 and adding a $45 installation fee?

• Vertical shrink by a factor of 0.5 and shift up by 45

• Vertical shrink by a factor of 2 and shift up by 45

• Vertical stretch by a factor of 2 and shift up by 45

• Vertical stretch by a factor of 0.5 and shift up by 45

What is the transformation applied to the function y = 60m to get y = 30m + 45?

• Vertical shrink by a factor of 2 and shift up by 45

• Vertical stretch by a factor of 2 and shift up by 45

• Vertical stretch by a factor of 0.5 and shift up by 45

• Vertical shrink by a factor of 0.5 and shift up by 45