Transformations of Functions

• The transformation reflects the graph of the function across the y-axis.

• The transformation shifts the graph to the right.

• The transformation stretches the graph vertically.

• The transformation compresses the graph horizontally.

What does the transformation @@f(kx)@@ do to the graph of a function?

• It reflects the graph vertically.

• It compresses or stretches the graph horizontally.

• It shifts the graph vertically.

• It rotates the graph around the origin.

Which transformation is represented by the equation @@(x - 2)^2@@?

• A shift of the graph of @@f(x) = x^2@@ 2 units to the right.

• A reflection of the graph of @@f(x) = x^2@@ across the x-axis.

• A vertical stretch of the graph of @@f(x) = x^2@@ by a factor of 2.

• A shift of the graph of @@f(x) = x^2@@ 2 units to the left.

What is the parent function of a quadratic function?

• @@f(x) = x^2@@

• @@f(x) = x@@

• @@f(x) = x^3@@

• @@f(x) = rac{1}{x}@@

What is the significance of the coefficient in front of @@f(x)@@, such as in @@g(x) = kf(x)@@?

• It determines the horizontal shift of the graph.

• It affects the vertical stretch or shrink of the graph. If @@k > 1@@, it stretches; if @@0 < k < 1@@, it shrinks.

• It changes the color of the graph.

• It has no effect on the graph.

What is the effect of subtracting a constant from the input of a function, such as in @@f(x - c)@@?

• It shifts the graph vertically.

• It shifts the graph horizontally; if @@c > 0@@, the graph shifts right; if @@c < 0@@, it shifts left.

• It reflects the graph across the x-axis.

• It stretches the graph vertically.

What does the transformation @@f(x) + 3@@ do to the graph?

• This transformation shifts the graph of the function down by 3 units.

• This transformation shifts the graph of the function up by 3 units.

• This transformation reflects the graph across the x-axis.

• This transformation stretches the graph vertically by a factor of 3.

• The transformation shifts the graph of the function 2 units to the right.

• The transformation shifts the graph of the function 2 units to the left.

• The transformation reflects the graph of the function across the x-axis.

• The transformation stretches the graph of the function vertically by a factor of 2.

What is the effect of adding a constant to a function, such as in @@f(x) + c@@?

• It shifts the graph vertically.

• It shifts the graph horizontally.

• It reflects the graph across the x-axis.

• It stretches the graph vertically.

What does a vertical shrink of a function do?

• It multiplies the output values of the function by a factor greater than 1, making the graph taller.

• It multiplies the output values of the function by a factor between 0 and 1, making the graph shorter.

• It shifts the graph of the function to the left or right.

• It reflects the graph of the function across the x-axis.