Pre-Calculus Review (Ch 1,2,3)

A comprehensive set of flashcards covering key concepts from Pre-Calculus topics including functions, transformations, polynomials, and equations.

What are the symmetric points with respect to the x-axis, y-axis, and origin for a given point?

The symmetric points can be found by changing the sign of the y-coordinate for x-axis, the sign of the x-coordinate for y-axis, and changing both coordinates for origin.

How do you determine if two functions are inverse functions?

Two functions are inverses if, for each function, f(g(x)) = x and g(f(x)) = x.

What is the nature of the roots?

The nature of the roots can be determined by the discriminant of a polynomial or the behavior of its graph.

How do you find the exponential function to model data points?

Use regression analysis or fit an exponential model to the given data points.

What transformation results from compressing a graph horizontally by a factor of 2?

The function g(x) = f(2x) compresses the graph of f horizontally by a factor of 2.

How do you find the domain and asymptotes of a function?

Identify restrictions on x (like denominators becoming zero) for the domain and analyze horizontal and vertical limits for asymptotes.

How do you determine the maximum number of real zeros of a polynomial function?

The maximum number of real zeros is given by the degree of the polynomial.

What does it mean if a function has an inverse?

A function has an inverse if it passes the horizontal line test, ensuring that each y-value corresponds to only one x-value.

What is the half-life formula used to calculate the decay of a radioactive sample?

The half-life formula is typically A(t) = A0(1/2)^(t/h), where A0 is the initial amount, t is time, and h is the half-life.

What are the intercepts, domain, range, symmetry, and end behavior of a polynomial function?

Intercepts are points where the function meets axes, domain is all possible x-values, range is the possible output values, symmetry depends on the function's equation, and end behavior describes the direction the function approaches as x approaches ±∞.

How can you model investment growth under continuous compounding?

Use the formula A = Pe^(rt), where P is the principal amount, r is the interest rate, and t is time.

Identify the characteristics of even and odd functions.

Even functions are symmetric about the y-axis, while odd functions are symmetric about the origin.

What is the significance of using percent changes in exponential decay models?

Percent changes represent the rate at which a quantity decreases or grows, key for applications like interest and population models.

How does changing coefficients affect the graph of a polynomial function?

Changing coefficients can alter the steepness, direction, and number of turning points of the polynomial graph.

Explain how transformations affect the shape of the graph of a function.

Transformations can shift (translate), stretch, compress, or reflect the graph about axes or specific points.

How do you solve polynomial inequalities?

Graph the polynomial and determine the intervals where the expression is greater than or less than zero.