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 a constant rate of change and can be expressed in 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 a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its rate of change is not constant, and it can be represented by equations that include exponents, logarithms, or other non-linear terms.

Tags

CCSS.8.F.A.3

Front

How do you determine the rate of change in a function?

Back

The rate of change in a function is determined by calculating the difference in the y-values divided by the difference in the x-values (rise over run) between two points on the graph.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph intersects the y-axis. It is represented as (0, b) in the equation y = mx + b.

Front

What does it mean for a function to have a greater rate of change?

Back

A function with a greater rate of change increases or decreases more rapidly than another function. This is often indicated by a steeper slope in the graph.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference in the y-values for equal intervals in the x-values. If the differences are not constant, the function is nonlinear.

Tags

CCSS.8.F.A.3

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Tags

CCSS.8.EE.B.5

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function. A positive slope means the function is increasing, while a negative slope means it is decreasing.

Tags

CCSS.8.EE.B.5

Front

How can you graph a linear function?

Back

To graph a linear function, you can plot the y-intercept on the y-axis and use the slope to find another point. Draw a straight line through these points.

Front

What are some common forms of nonlinear functions?

Back

Common forms of nonlinear functions include quadratic functions (y = ax^2 + bx + c), exponential functions (y = a * b^x), and logarithmic functions (y = log_b(x)).