Quiz Parent Functions and Transformations

What is the difference between a linear function and a quadratic function?

• A linear function has a constant rate of change and is represented by a straight line (y = mx + b), while a quadratic function has a variable rate of change and is represented by a parabola (y = ax^2 + bx + c).

• A linear function is represented by a curve, while a quadratic function is represented by a straight line.

• A linear function can have multiple outputs for a single input, while a quadratic function has only one output for each input.

• A linear function is always increasing, while a quadratic function can be increasing or decreasing.

What is a vertical shrink in transformations?

• A vertical shrink occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter.

• A vertical shrink occurs when the input values of a function are increased, stretching the graph vertically.

• A vertical shrink occurs when the graph is flipped upside down, inverting the function.

• A vertical shrink occurs when the graph is translated upwards by a constant value.

What is the general form of a quadratic function?

• @@f(x) = ax^2 + bx + c@@, where a, b, and c are constants.

• @@f(x) = ax^2 - bx + c@@, where a, b, and c are constants.

• @@f(x) = ax^2 + b + c@@, where a, b, and c are constants.

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

What is the effect of a negative sign in front of a function?

• It reflects the graph across the x-axis.

• It shifts the graph to the right.

• It stretches the graph vertically.

• It changes the graph's color.

What is a parent function?

• A function that has no variables.

• The simplest form of a function type, which serves as a foundation for more complex functions.

• A function that only includes constants.

• A function that is always increasing.

• Shrinks by a factor of 1/2, shifts right 1 unit, and shifts down 1 unit.

• Stretches by a factor of 2, shifts left 1 unit, and shifts up 1 unit.

• Shrinks by a factor of 1/2, shifts left 1 unit, and shifts up 1 unit.

• Stretches by a factor of 2, shifts right 1 unit, and shifts down 1 unit.

What is the parent function of a cubic function?

• @@f(x) = x^2@@

• @@f(x) = x^3@@

• @@f(x) = x@@

• @@f(x) = x^4@@

What is the parent function of a square root function?

• @@f(x) = ext{sqrt}(x)@@

• @@f(x) = x^2@@

• @@f(x) = x^3@@

• @@f(x) = rac{1}{x}@@

What does shifting a graph down mean?

• Adding a value to the output variable (y), which moves the graph vertically.

• Subtracting a value from the output variable (y), which moves the graph vertically.

• Multiplying the output variable (y) by a negative value, which reflects the graph.

• Dividing the output variable (y) by a positive value, which compresses the graph.

Which parent function matches the graph of @@y = x^2@@?

• Linear function

• Quadratic function

• Cubic function

• Exponential function