Transformations of Functions

What does the equation @@f(x + 3)@@ indicate about the graph?

• The graph is translated 3 units to the left.

• The graph is translated 3 units to the right.

• The graph is reflected over the x-axis.

• The graph is stretched vertically by a factor of 3.

What does a vertical shrink by a factor of 1/2 do to the graph of a function?

• It compresses the graph towards the x-axis, making it shorter.

• It stretches the graph away from the x-axis, making it taller.

• It reflects the graph over the x-axis, flipping it upside down.

• It shifts the graph to the right, increasing its width.

Which equation represents a quadratic function translated up 5 units?

• @@y = x^2 + 5@@

• @@y = x^2 - 5@@

• @@y = x^2 + 2@@

• @@y = x^2 + 10@@

• The graph is translated 1 unit down.

• The graph is translated 1 unit up.

• The graph is reflected over the x-axis.

• The graph is stretched vertically by a factor of 2.

What does a vertical stretch by a factor of 2 do to the graph of a function?

• It makes the graph taller, stretching it away from the x-axis.

• It compresses the graph towards the x-axis.

• It reflects the graph across the x-axis.

• It shifts the graph upwards by 2 units.

How does the equation @@f(x + 7)@@ transform the graph?

• The graph of the function is translated 7 units to the left.

• The graph of the function is reflected over the x-axis.

• The graph of the function is stretched vertically by a factor of 7.

• The graph of the function is translated 7 units to the right.

What does the equation @@f(x) - 6@@ represent?

• The graph of the function is translated 6 units down.

• The graph of the function is translated 6 units up.

• The graph of the function is reflected over the x-axis.

• The graph of the function is stretched vertically by a factor of 6.

What is the effect of the equation @@f(x) + 3@@ on the graph?

• The graph of the function is translated 3 units up.

• The graph of the function is translated 3 units down.

• The graph of the function is reflected over the x-axis.

• The graph of the function is stretched vertically by a factor of 3.

What does the transformation @@f(-x)@@ represent?

• It reflects the graph across the y-axis.

• It reflects the graph across the x-axis.

• It translates the graph to the right.

• It stretches the graph vertically.

What is the transformation described by the equation @@f(x - 1)@@?

• The graph is translated 1 unit to the right.

• The graph is reflected over the x-axis.

• The graph is stretched vertically by a factor of 2.

• The graph is translated 1 unit to the left.