Function Transformations

What is the effect of a horizontal stretch on a function?

• A horizontal stretch makes the graph narrower.

• A horizontal stretch occurs when the input values of a function are multiplied by a factor between 0 and 1, making the graph wider.

• A horizontal stretch has no effect on the graph of the function.

• A horizontal stretch flips the graph over the x-axis.

What is the significance of the vertex in a quadratic function?

• The vertex is the point where the parabola intersects the x-axis.

• The vertex is the highest or lowest point of the parabola, representing the maximum or minimum value of the function.

• The vertex indicates the direction in which the parabola opens.

• The vertex is the midpoint of the line segment connecting the x-intercepts.

What does f(x - h) represent in terms of transformation?

• A horizontal shift of the graph to the right by h units.

• A vertical shift of the graph upwards by h units.

• A reflection of the graph across the x-axis.

• A compression of the graph by a factor of h.

What does the transformation f(x) = f(x) + k do to the graph?

• Shifts the graph vertically by k units.

• Shifts the graph horizontally by k units.

• Reflects the graph over the x-axis.

• Stretches the graph vertically by a factor of k.

What is a vertical stretch of a function?

• A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

• A vertical stretch occurs when the input values of a function are multiplied by a factor greater than 1, making the graph wider.

• A vertical stretch occurs when the output values of a function are added to a constant, shifting the graph upwards.

• A vertical stretch occurs when the function is reflected over the x-axis, inverting the graph.

What does f(x + h) represent in terms of transformation?

• A horizontal shift of the graph to the left by h units.

• A vertical shift of the graph upwards by h units.

• A reflection of the graph across the x-axis.

• A compression of the graph by a factor of h.

What is the parent function of a quadratic function?

• f(x) = x

• f(x) = x²

• f(x) = x³

• f(x) = 2x²

What is a function transformation?

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

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

• A function transformation is a technique used to integrate functions more easily.

• A function transformation is a way to simplify a function by removing variables.

What does a vertical shift of a function mean?

• A vertical shift moves the graph of the function up or down without changing its shape.

• A vertical shift changes the slope of the function.

• A vertical shift reflects the graph across the x-axis.

• A vertical shift alters the function's domain.

What is the general form of a quadratic function?

• f(x) = ax² + bx + c, where a, b, and c are constants.

• f(x) = ax³ + bx² + c, where a, b, and c are constants.

• f(x) = a + b + c, where a, b, and c are constants.

• f(x) = ax² - bx + c, where a, b, and c are constants.