Compare Linear, Quadratic, and Exponential Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic function?

Back

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

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.

Front

How can you identify an exponential function from its equation?

Back

An exponential function can be identified by the variable being in the exponent, such as in f(x) = 2(5)^x.

Front

What are the characteristics of a linear function's graph?

Back

The graph of a linear function is a straight line, has a constant slope, and can intersect the y-axis at one point.

Front

What are the characteristics of a quadratic function's graph?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards, and has a vertex, axis of symmetry, and may have zero, one, or two x-intercepts.

Front

What are the characteristics of an exponential function's graph?

Back

The graph of an exponential function increases or decreases rapidly, has a horizontal asymptote, and never touches the x-axis.

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, represented as (0, f(0)).

Front

What is the x-intercept of a function?

Back

The x-intercept is the point where the graph of a function crosses the x-axis, represented as (x, 0).

Front

What is an axis of symmetry?

Back

An axis of symmetry is a line that divides a figure into two mirror-image halves. For parabolas, it is a vertical line through the vertex.