AP PreCalculus Unit 1 Review

Front

What is the domain of the function g(x) = (x^3 + 8x^2 + 12x) / (x^2 + 2x - 24)?

Back

The domain of g is all real numbers x where x ≠ 6 and x ≠ 4.

Front

What does it mean for a graph to be concave down?

Back

A graph is concave down if the average rates of change over consecutive equal-length input-value intervals are decreasing.

Front

Given the functions f(x) = 2x^2 - 3x + 1 and g(x) = x^2 - x + 9, how do you find the intervals where f(x) ≤ g(x)?

Back

To find the intervals where f(x) ≤ g(x), set the inequality 2x^2 - 3x + 1 ≤ x^2 - x + 9 and solve for x.

Front

What is the least possible degree of a polynomial function g?

Back

The least possible degree of g is determined by the highest power of x in its expression; in this case, it is 3.

Front

How do you calculate the average rate of change of a function f(x) over an interval [a, b]?

Back

The average rate of change of f(x) over [a, b] is calculated as (f(b) - f(a)) / (b - a).

Front

What is the significance of the average rate of change in a function?

Back

The average rate of change indicates how much the function's output changes on average for each unit change in the input over a specified interval.

Front

What are the steps to determine the domain of a rational function?

Back

To determine the domain of a rational function, identify values that make the denominator zero and exclude them from the set of all real numbers.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What does it mean for a polynomial to be concave up?

Back

A polynomial is concave up if the average rates of change over consecutive equal-length input-value intervals are increasing.

Front

How do you find the intervals of a function where it is increasing or decreasing?

Back

To find intervals where a function is increasing or decreasing, calculate the derivative and determine where it is positive (increasing) or negative (decreasing).