Function Families

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 a positive real number, and x is the exponent. The base b determines the growth or decay rate.

Front

What are the characteristics of a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

What is a quadratic function?

Back

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

Front

What defines a linear absolute value function?

Back

A linear absolute value function is a function that combines a linear function with an absolute value, typically expressed as f(x) = a|x - h| + k, where (h, k) is the vertex of the V-shaped graph.

Tags

CCSS.HSF-IF.C.7D

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions based on the input value. It consists of multiple sub-functions, each applying to a specific interval of the domain.

Front

How can you identify an exponential function from a graph?

Back

An exponential function graph shows rapid growth or decay, characterized by a curve that rises or falls sharply. It does not cross the x-axis and approaches it asymptotically.

Tags

CCSS.HSF-IF.C.7E

Front

What is the general form of a linear piecewise function?

Back

A linear piecewise function is defined by different linear equations for different intervals of the input variable. For example, f(x) = { m1x + b1 for x < c, m2x + b2 for x ≥ c }.

Tags

CCSS.HSF-IF.C.7B

Front

What are the key features of a quadratic function's graph?

Back

The graph of a quadratic function is a parabola. Key features include the vertex (the highest or lowest point), axis of symmetry, and x-intercepts (roots) where the graph crosses the x-axis.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function represents the maximum or minimum point of the parabola, depending on the direction it opens. It is found at the point (h, k) in the vertex form f(x) = a(x - h)^2 + k.

Front

How do you determine the slope of a linear function?

Back

The slope of a linear function is determined by the ratio of the change in y to the change in x (rise over run) between any two points on the line, often represented as m in the equation f(x) = mx + b.

Tags

CCSS.8.EE.B.5