Function Families

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

Identify the general form of a linear function.

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

What characterizes a quadratic function?

Back

A quadratic function is characterized by its standard form y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of an absolute value function?

Back

The standard form of an absolute value function is y = |x - h| + k, where (h, k) is the vertex of the graph.

Front

Describe the general form of a cubic function.

Back

The general form of a cubic function is y = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

What is the domain of a linear function?

Back

The domain of a linear function is all real numbers, as there are no restrictions on the input values.

Front

What is the range of a quadratic function?

Back

The range of a quadratic function is all real numbers greater than or equal to the vertex value if a > 0, or less than or equal to the vertex value if a < 0.

Front

How do you determine the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form y = ax^2 + bx + c can be found using the formula x = -b/(2a) and then substituting this x value back into the function to find y.

Front

What is the significance of the leading coefficient in a cubic function?

Back

The leading coefficient of a cubic function determines the end behavior of the graph; if it is positive, the graph rises to the right, and if negative, it falls to the right.

Front

What is the shape of the graph of an absolute value function?

Back

The graph of an absolute value function has a V-shape, with the vertex at the point (h, k).