Exploring Adding and Subtracting Rational Expressions

The video tutorial covers the comparison between quadratic and exponential functions, emphasizing that exponential functions eventually grow faster. It includes a warm-up activity to order expressions, an activity to compare growth patterns, and a detailed analysis of growth steps. Equations for both patterns are derived, and growth factors are compared to illustrate why exponential functions surpass quadratics over time. The session concludes with a cool down activity.

Which function type grows faster over time?

• Both grow at the same rate

• Exponential functions

• It depends on the function's coefficients

• Quadratic functions

What is the base number of an exponential function critical for?

• Determining its growth rate

• Solving for its exponents

• Finding its intercepts

• Calculating its derivative

How does the area of squares change in Pattern A?

• It grows by the square of the step number

• It increases by one square unit each step

• It remains constant

• It doubles each step

What signifies an exponential function?

• A variable base minus a constant exponent

• A variable base raised to a constant exponent

• A constant base plus a variable exponent

• A constant base raised to a variable exponent

What is the growth factor in an exponential function?

• The coefficient of the base

• The difference between consecutive outputs

• The ratio of consecutive outputs

• The sum of the base and exponent

Why do exponential functions grow faster than quadratic functions?

• Due to their larger exponents

• Because of their constant growth factor

• Because of their higher coefficients

• Due to their variable growth factor

What does the graph comparison between quadratic and exponential functions show?

• Exponential functions always start higher

• Quadratic functions eventually overtake exponential functions

• Exponential functions overtake quadratic functions over time

• Both functions intersect at multiple points

How can you determine the growth factor of a pattern?

• By adding consecutive outputs

• By dividing a term by its preceding term

• By multiplying the base by the exponent

• By subtracting the exponent from the base

What mistake did Tyler make in his conclusion about 5x^2 and 2^x?

• He confused the functions' bases and exponents

• He correctly predicted the growth patterns

• He overestimated the growth of 5x^2

• He underestimated the growth of 2^x

Why is the growth factor important in comparing functions?

• It affects the function's coefficients

• It determines the function's intercepts

• It influences the function's rate of growth

• It changes the function's domain and range