Transformation of Functions

What does it mean to translate a function?

• Translating a function means shifting its graph horizontally and/or vertically without changing its shape.

• Translating a function means reflecting its graph across the x-axis.

• Translating a function means stretching its graph vertically or horizontally.

• Translating a function means rotating its graph around the origin.

What is the effect of the term (x - h) in a quadratic function?

• The term (x - h) indicates a vertical shift upwards by h units if h is positive, and downwards if h is negative.

• The term (x - h) indicates a horizontal shift to the right by h units if h is positive, and to the left if h is negative.

• The term (x - h) indicates a reflection over the x-axis if h is positive, and over the y-axis if h is negative.

• The term (x - h) indicates a stretch of the graph by a factor of h if h is positive, and a compression if h is negative.

What does the coefficient 'a' in a quadratic function affect?

• The height of the vertex of the parabola.

• The width and direction of the parabola; if a > 1, the parabola is narrower, and if a < 1, it is wider. If a < 0, the parabola opens downwards.

• The color of the graph of the function.

• The position of the parabola on 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.

How does the equation y = x² + 5 represent a transformation?

• It represents a horizontal translation of the parent function y = x², shifted right 5 units.

• It represents a vertical translation of the parent function y = x², shifted up 5 units.

• It represents a reflection of the parent function y = x² across the x-axis.

• It represents a compression of the parent function y = x² by a factor of 5.

Describe the transformation of f(x) = (x - 3)² + 5.

• This function represents a leftward shift of 3 units and a downward shift of 5 units from the parent function y = x².

• This function represents a rightward shift of 3 units and an upward shift of 5 units from the parent function y = x².

• This function represents a rightward shift of 3 units and a downward shift of 5 units from the parent function y = x².

• This function represents a leftward shift of 3 units and an upward shift of 5 units from the parent function y = x².

How do you identify the direction a parabola opens?

• A parabola opens upwards if the leading coefficient (a) is positive and downwards if it is negative.

• A parabola opens downwards if the leading coefficient (a) is positive and upwards if it is negative.

• A parabola opens to the left if the leading coefficient (a) is positive and to the right if it is negative.

• A parabola opens upwards if the vertex is above the x-axis and downwards if it is below.

How does the transformation f(x) = 3|x + 8| affect the parent function?

• It stretches the parent function vertically by a factor of 3 and shifts it left by 8 units.

• It compresses the parent function vertically by a factor of 3 and shifts it right by 8 units.

• It reflects the parent function across the x-axis and shifts it down by 8 units.

• It stretches the parent function horizontally by a factor of 3 and shifts it up by 8 units.

What does the absolute value in f(x) = 3|x + 8| indicate?

• The absolute value indicates that the function will reflect any negative values of (x + 8) above the x-axis, creating a V-shaped graph.

• The absolute value indicates that the function will only take positive values of (x + 8), ignoring any negative inputs.

• The absolute value indicates that the function will shift the graph to the left by 8 units.

• The absolute value indicates that the function will have a maximum value at x = -8.

What is the parent function of a quadratic equation?

• f(x) = x

• f(x) = x²

• f(x) = x³

• f(x) = 2x²