Transformations of Functions

What is the effect of multiplying a function by a factor greater than 1, such as g(x) = 2f(x)?

• It reflects the graph across the x-axis.

• It vertically stretches the graph away from the x-axis.

• It compresses the graph towards the x-axis.

• It shifts the graph horizontally to the right.

What is the transformation represented by g(x) = f(x - 2)?

• A horizontal shift of the graph of f(x) to the left by 2 units.

• A horizontal shift of the graph of f(x) to the right by 2 units.

• A vertical shift of the graph of f(x) upwards by 2 units.

• A vertical shift of the graph of f(x) downwards by 2 units.

What does the term 'vertical shift' refer to in function transformations?

• A vertical shift refers to moving the graph of a function up or down.

• A vertical shift refers to changing the slope of the function.

• A vertical shift refers to reflecting the graph across the x-axis.

• A vertical shift refers to stretching the graph horizontally.

How does the equation f(x) = (x - h)^2 + k transform the graph of f(x) = x^2?

• The graph is reflected over the x-axis.

• The graph is shifted left by h units and down by k units.

• The graph is shifted right by h units and up by k units.

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

What is the effect of a negative sign in front of a function, such as g(x) = -f(x)?

• A negative sign in front of a function reflects the graph over the x-axis.

• A negative sign in front of a function shifts the graph to the left.

• A negative sign in front of a function stretches the graph vertically.

• A negative sign in front of a function changes the function's domain.

What does it mean to reflect a graph over the y-axis?

• It means to flip the graph upside down.

• It means to shift the graph to the right.

• It means to replace x with -x in the function, resulting in the point (-x, y) for every point (x, y).

• It means to stretch the graph horizontally.

How do you describe the transformation from f(x) = x^3 to g(x) = x^3 - 5?

• A vertical shift up by 5 units.

• A vertical shift down by 5 units.

• A horizontal shift left by 5 units.

• A horizontal shift right by 5 units.

What is a transformation of a function?

• A transformation of a function refers to the changes made to the graph of a function, which can include shifts, reflections, stretches, and compressions.

• A transformation of a function is a method to calculate the derivative of a function.

• A transformation of a function is a technique used to find the roots of a polynomial.

• A transformation of a function is a way to simplify complex functions into linear functions.

What does it mean to shift a graph left or right?

• It involves adding or subtracting a value from the input (x) of the function.

• It means changing the scale of the graph vertically.

• It refers to rotating the graph around the origin.

• It indicates reflecting the graph across the y-axis.

What does it mean to reflect a graph over the x-axis?

• It means to shift the graph upwards by a certain value.

• It means to reflect the graph over the y-axis.

• It means that for every point (x, y), the corresponding point will be (x, -y).

• It means to stretch the graph vertically.