Pre-Calculus Spring Review 2024

Front

What is the formula for exponential growth with an initial amount and a percentage increase?

Back

The formula is A = P(1 + r)^t, where A is the amount after time t, P is the initial amount, r is the growth rate (as a decimal), and t is time.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

How do you find the roots of a polynomial?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero. They can be found by factoring, using the quadratic formula, or graphing.

Front

What is a horizontal asymptote in a rational function?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches infinity or negative infinity.

Front

How do you factor a polynomial expression?

Back

To factor a polynomial, look for common factors, use grouping, or apply special factoring techniques like difference of squares or perfect square trinomials.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases by a percentage over time, while linear growth increases by a fixed amount.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function and influences the shape of its graph.

Front

What is the relationship between the degree of a polynomial and the number of roots it can have?

Back

A polynomial of degree n can have up to n roots, counting multiplicities.

Front

What is the formula for finding the horizontal asymptote of a rational function?

Back

For rational functions, if the degrees of the numerator and denominator are equal, the horizontal asymptote is y = a/b, where a and b are the leading coefficients.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, the value of f(x) also increases.