Question

identify the parent function and describe the transformations.

1. $f(x) = (x + 4)^3$

parent:
transformation:

1. $f(x) = -2|x - 4|$

parent:
transformation:

1. $f(x) = \frac{1}{x} - 18$

parent:
transformation:

1. $f(x) = -\sqrt{x + 1} - 6$

parent:
transformation:

Explanation:

For each function, the parent function is the simplest form of the given function type. Transformations are identified by comparing the given function to the parent function, using rules for horizontal/vertical shifts, reflections, and stretches/compressions.

1. Problem 5: The function is a cubic function. The parent cubic function is $f(x)=x^3$. Replacing $x$ with $x+4$ shifts the graph left 4 units.
2. Problem 6: The function is an absolute value function. The parent absolute value function is $f(x)=|x|$. The coefficient $-2$ reflects over the x-axis and vertically stretches by a factor of 2; replacing $x$ with $x-4$ shifts the graph right 4 units.
3. Problem 7: The function is a reciprocal function. The parent reciprocal function is $f(x)=\frac{1}{x}$. Subtracting 18 shifts the graph down 18 units.
4. Problem 8: The function is a square root function. The parent square root function is $f(x)=\sqrt{x}$. The negative sign reflects over the x-axis; replacing $x$ with $x+1$ shifts left 1 unit; subtracting 6 shifts down 6 units.

Answer:

1. Parent: $f(x)=x^3$

Transformation: Horizontal shift left 4 units

1. Parent: $f(x)=|x|$

Transformation: Reflection over the x-axis, vertical stretch by a factor of 2, horizontal shift right 4 units

1. Parent: $f(x)=\frac{1}{x}$

Transformation: Vertical shift down 18 units

1. Parent: $f(x)=\sqrt{x}$

Transformation: Reflection over the x-axis, horizontal shift left 1 unit, vertical shift down 6 units