Exploring Basic Parent Functions

Denise Del introduces parent functions, focusing on their focal points, domain, and range. She covers linear, quadratic, cubic, square root, and absolute value functions, emphasizing the importance of understanding their properties. The lesson concludes with a summary of key points.

What is a focal point in the context of parent functions?

• A point where the graph intersects the x-axis

• A point that must be memorized for each graph

• A point where the graph intersects the y-axis

• A point that is always at (1,1)

Where does the focal point lie for the parent function y = x^2?

• (0,1)

• (1,0)

• (1,1)

• (0,0)

Which parent function is referred to as 'disco fever'?

• y = x

• y = x^2

• y = x^3

• y = |x|

What does the graph of y = √x resemble?

• A full parabola

• A cubic curve

• A sideways parabola

• A straight line

Which parent function has a domain restriction?

• y = x

• y = x^2

• y = x^3

• y = √x

What is the domain of the function y = √x?

• All real numbers

• x ≥ 0

• x ≤ 0

• x ≠ 0

What is the range of the linear function y = x?

• y ≤ 0

• y ≠ 0

• y ≥ 0

• All real numbers

Which of the following functions has a range of y ≥ 0?

• y = x

• y = x^3

• y = |x|

• y = x^2

Why can't the range of the absolute value function y = |x| be negative?

• Because it is always positive

• Because it is always zero

• Because it is always negative

• Because it is always undefined

What is the range of the function y = x^2?

• All real numbers

• y ≠ 0

• y ≤ 0

• y ≥ 0