Comparing 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 y = 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 y = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent. It grows or decays at a constant rate.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax^2 + bx + c, where a, b, and c are constants. Its graph is a parabola.

Front

How can you identify a linear equation?

Back

A linear equation can be identified by its highest degree being 1, meaning it has no exponents greater than 1. It can be written in the form y = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope of a line represent?

Back

The slope of a line 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?

Back

The y-intercept is the point where the graph of a function crosses the y-axis. It is the value of y when x = 0.

Front

What is the difference between growth and decay in exponential functions?

Back

Exponential growth occurs when the base b > 1, leading to an increase in value as x increases. Exponential decay occurs when 0 < b < 1, leading to a decrease in value as x increases.

Tags

CCSS.HSF-IF.C.8B

Front

What is a characteristic of quadratic functions?

Back

Quadratic functions have a U-shaped graph called a parabola, which can open upwards or downwards depending on the sign of the coefficient a.

Tags

CCSS.HSF-IF.C.7A

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing if its slope is positive (the graph rises as you move from left to right) and decreasing if its slope is negative (the graph falls as you move from left to right).

Front

What is the significance of the vertex in 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. It represents the maximum or minimum value of the function.