Parent Functions

Multiple Choice

What is the significance of understanding parent functions and their transformations in mathematics?

• To solve complex equations

• To understand the behavior of different functions

• To memorize mathematical formulas

• To perform arithmetic operations

Multiple Choice

What is the vertex form of a quadratic function?

• f(x) = a(x-h)^2 + k

• f(x) = ax^2 + bx + c

• f(x) = a(x-h)^3 + k

• f(x) = a√(x-h) + k

Multiple Choice

How does the domain of a square root function differ from that of a quadratic function?

• The domain of a square root function is [0, ∞), while a quadratic function is (-∞, ∞).

• The domain of a square root function is (-∞, ∞), while a quadratic function is [0, ∞).

• Both have the same domain.

• The domain of a square root function is (-∞, 0], while a quadratic function is (-∞, ∞).

Multiple Choice

Compare the end behavior of cubic and cube root functions.

• Both approach infinity as x approaches infinity.

• Cubic functions approach infinity, while cube root functions approach zero.

• Cubic functions approach zero, while cube root functions approach infinity.

• Both approach zero as x approaches infinity.

Fill in the Blanks

Write the equation of a cubic function in vertex form.

Open Ended

Describe the transformations necessary to transform the graph of \( f(x) \) (solid line) into that of \( g(x) \) (dashed line).

Multiple Choice

What transformations are applied to change $$f\left(x\right)=\sqrt[]{x}\ \ \ \ \ \ \ \ to\ \ \ g\left(x\right)=-3\sqrt[]{x}-1$$ ?

• Reflect over the x-axis, vertical stretch by 3, translate down 1

• Reflect over the y-axis, vertical compression by 3, translate up 1

• Reflect over the x-axis, vertical compression by 3, translate down 1

• Reflect over the y-axis, vertical stretch by 3, translate up 1

Multiple Choice

Which transformations are applied to $$f\left(x\right)=\left|x\right|\ to\ change\ to\ g\left(x\right)=\left|\frac{1}{2}\left(x-1\right)\right|+3$$

• Expand horizontally by a factor of 2, translate right 1 unit, translate up 3 units

• Compress horizontally by a factor of 2, translate left 1 unit, translate down 3 units

• Expand horizontally by a factor of 2, translate left 1 unit, translate up 3 units

• Compress horizontally by a factor of 2, translate right 1 unit, translate down 3 units

Multiple Choice

What is the domain of the quadratic parent function y = x^2?

• (-∞, ∞)

• [0, ∞)

• (-∞, 0]

• [0, 0]