Transformations of Parent Functions: Adding and Subtracting Rational Expressions

What is the first step in identifying the function from a graph?

• Determine the slope

• Check for vertical shifts

• Identify the parent function

• Look for horizontal shifts

Which of the following is a parent function for a quadratic graph?

• x^3

• sqrt(x)

• x^2

• |x|

If a quadratic function is shifted left by 1 unit and down by 3 units, what is the resulting function?

• (x - 1)^2 + 3

• (x - 1)^2 - 3

• (x + 1)^2 - 3

• (x + 1)^2 + 3

What is the parent function for an absolute value graph?

• sqrt(x)

• x^3

• |x|

• x^2

How do you represent a vertical flip in an absolute value function?

• Add a positive sign inside the function

• Add a positive sign outside the function

• Add a negative sign inside the function

• Add a negative sign outside the function

What is the parent function for a cubic graph?

• |x|

• x^3

• x^2

• sqrt(x)

If a cubic function is shifted right by 4 units and down by 1 unit, what is the resulting function?

• (x + 4)^3 - 1

• (x - 4)^3 - 1

• (x + 4)^3 + 1

• (x - 4)^3 + 1

What is the parent function for a square root graph?

• x^2

• sqrt(x)

• x^3

• |x|

How do you represent a vertical shrink by a factor of 1/2 in a square root function?

• Add 1/2 to the function

• Multiply the function by 2

• Divide the function by 2

• Multiply the function by 1/2

What is the general form of a linear function?

• y = mx + b

• y = ax^2 + bx + c

• y = a|x| + b

• y = a sqrt(x) + b