AP Precalculus: Unit 2 Review

Front

What is the explicit rule for the arithmetic sequence -10, -3, 4, 11,...?

Back

The explicit rule is a_n = 7n - 17.

Front

What is an equivalent form of the equation y=6⋅4^x?

Back

An equivalent form is y=6⋅16^{(\frac{x}{2})}.

Front

How do you calculate the average rate of change from 20 to 40 minutes?

Back

The average rate of change is -2 gallons per minute.

Front

What are the x-intercepts of the quadratic equation y = 3x^2 - 12x + 9?

Back

There are no real roots.

Front

What transformations occur in the function g(x) = -2^(x+3) - 6 from f(x) = 2^x?

Back

The transformations are: reflects over x-axis, left 3, down 6.

Front

Define an arithmetic sequence.

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term is given by a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which each term is multiplied to get the next term.

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term is given by a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What does it mean for a function to reflect over the x-axis?

Back

Reflecting over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.