Combining Functions by Dividing

This lesson covers how to create a new function by dividing two functions. It explains finding zeros of a function through factoring and graphing, addresses common misunderstandings in simplification, and demonstrates dividing functions f(x) by g(x) and g(x) by f(x). The lesson highlights the importance of handling undefined points and defining the domain of the resulting function. Graphical representations are used to illustrate concepts, emphasizing the need to avoid division by zero.

What are the zeros of a function?

• The y values that make x equal to 0

• The x values that make y equal to 0

• The x values that make y equal to 1

• The y values that make x equal to 1

Why is it important to find the zeros of a function when dividing functions?

• To determine the slope of the function

• To find the x-intercepts

• To determine the range of the function

• To simplify the function

What is a common misunderstanding when simplifying expressions?

• That the simplified expression is always equal to the original for all x

• That the simplified expression is never equal to the original

• That the simplified expression is only equal to the original at x=0

• That the simplified expression is equal to the original only for positive x

What must be ensured when dividing two functions?

• The numerator is not zero

• The denominator is not zero

• Both numerator and denominator are zero

• The denominator is always positive

What is the domain of f divided by g(x)?

• All real numbers except where f(x) is zero

• All real numbers except where g(x) is zero

• All real numbers

• All real numbers except where both f(x) and g(x) are zero

When dividing g(x) by f(x), what must be considered?

• The zeros of both f(x) and g(x)

• The zeros of neither f(x) nor g(x)

• The zeros of g(x)

• The zeros of f(x)

What happens to the graph of g divided by f(x) at x values where the denominator is zero?

• The graph has a peak

• The graph has a hole

• The graph has a vertical line

• The graph is continuous