Function and Parent Functions - Transformations

What transformation occurs when f(x) is replaced with f(x) + 5?

• Vertical translation down by 5 units.

• Vertical translation up by 5 units.

• Horizontal translation left by 5 units.

• Horizontal translation right by 5 units.

What is the range of the function f(x) = -x^2?

• All real numbers

• All positive numbers

• All nonpositive numbers, represented as @@y \le 0@@ or @@(-\infty, 0]@@

• All negative numbers

What does a vertical compression by a factor of 1/2 do to a function?

• It reduces the height of the graph by half, making it flatter.

• It doubles the height of the graph, making it steeper.

• It shifts the graph to the left by half its width.

• It reflects the graph across the x-axis.

What transformation occurs when f(x) is replaced with 2⋅f(x)?

• Vertical Stretch by a factor of 2.

• Vertical Compression by a factor of 2.

• Horizontal Stretch by a factor of 2.

• Reflection over the x-axis.

What is the effect of a reflection across the x-axis on a function?

• It flips the graph of the function over the x-axis.

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

• It stretches the graph of the function vertically.

• It rotates the graph of the function 180 degrees.

How does the transformation f(x) = -f(x) affect the graph?

• It reflects the graph across the x-axis.

• It shifts the graph to the right.

• It stretches the graph vertically.

• It reflects the graph across the y-axis.

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

• It translates the graph horizontally to the right by c units.

• It translates the graph vertically upwards by c units.

• It reflects the graph across the x-axis.

• It stretches the graph horizontally by a factor of c.

What is the domain of the function f(x) = x^2?

• All real numbers, represented as @@(-\infty, \infty)@@

• Only positive real numbers, represented as @@[0, \infty)@@

• Only negative real numbers, represented as @@(-\infty, 0)@@

• Only integers, represented as @@\mathbb{Z}@@

What is a parent function?

• A parent function is the simplest form of a function type, which serves as a foundation for more complex functions.

• A parent function is a function that has no variables.

• A parent function is a function that only includes constants.

• A parent function is a function that can only be graphed in one quadrant.

What is the domain of the function f(x) = 1/x?

• All real numbers

• All real numbers except x = 1

• All real numbers except x = 0, represented as @@(-\infty, 0) \cup (0, \infty)@@

• All real numbers except x = -1