Linear, Exponential and Quadratic 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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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 (a positive real number), and x is the exponent. It shows rapid growth or decay.

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

Identify the general form of a linear function.

Back

The general form of a linear function is f(x) = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

Identify the general form of a quadratic function.

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c.

Front

What is the shape of the graph of a quadratic function?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient a.

Tags

CCSS.HSF-IF.C.7A

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the linear function f(x) = mx + b.

Front

How can you determine if a function is exponential from a table of values?

Back

If the ratio of consecutive outputs (y-values) is constant, the function is exponential.

Tags

CCSS.HSF-LE.A.1A

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.