Big Review! AP Precalculus

Front

What does it mean for a graph to transition from concave down to concave up?

Back

This indicates a change in the curvature of the graph, where the rate of change of the slope is increasing.

Front

How do you factor the expression x² - 25?

Back

The expression can be factored as (x + 5)(x - 5), which is a difference of squares.

Front

What is the logarithmic identity for log(m³/n)?

Back

The identity is log(m³/n) = 3log(m) - log(n).

Front

What is the definition of slope in a mathematical context?

Back

The slope is defined as the rate of change of a function, representing how much the output value changes for a change in the input value.

Front

How do you find the limit of a rational function as x approaches a certain value?

Back

To find the limit, simplify the function if possible, and then substitute the value of x into the simplified function.

Front

What is the significance of concavity in a function's graph?

Back

Concavity indicates the direction of the curvature of the graph, which can provide information about the function's behavior and its inflection points.

Front

What is the difference between a local maximum and a local minimum?

Back

A local maximum is a point where the function value is higher than all nearby points, while a local minimum is where the function value is lower than all nearby points.

Front

What is the derivative of a function, and how is it related to the slope?

Back

The derivative of a function at a point gives the slope of the tangent line to the graph at that point.

Front

What is the purpose of factoring polynomials?

Back

Factoring polynomials simplifies expressions and helps in solving equations by finding the roots.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other; if y = a^x, then x = log_a(y).