Parent Functions

Front

What is a cubic function?

Back

A cubic function is a polynomial function of degree three, typically in the form f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

What is a linear function?

Back

A linear function is a polynomial function of degree one, represented as f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (b > 0, b ≠ 1), and x is the exponent.

Front

What is a reciprocal function?

Back

A reciprocal function is defined as f(x) = 1/x, where x ≠ 0. It represents a hyperbola and has vertical and horizontal asymptotes.

Front

What is an absolute value function?

Back

An absolute value function is defined as f(x) = |x|, which outputs the non-negative value of x, effectively reflecting negative values across the x-axis.

Front

What is the general shape of a cubic function graph?

Back

The graph of a cubic function typically has an S-shape, with one or two turning points, and can extend to positive or negative infinity.

Front

What are the key characteristics of a linear function graph?

Back

The graph of a linear function is a straight line, characterized by a constant slope and a y-intercept.

Front

What is the growth behavior of an exponential function?

Back

Exponential functions grow rapidly as x increases if the base is greater than 1, and decay rapidly if the base is between 0 and 1.

Front

What are the asymptotes of a reciprocal function?

Back

The reciprocal function has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.

Front

How does the graph of an absolute value function behave?

Back

The graph of an absolute value function forms a V-shape, with the vertex at the origin (0,0) and opens upwards.