Representing Functions; Linear vs Nonlinear Functions

Front

What is a function?

Back

A function is a relationship between two sets of values where each input (x) has exactly one output (y).

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line. Its rate of change varies and can be represented by equations that include exponents, roots, or other non-linear terms.

Front

How do you determine if a function is linear or nonlinear from a table of values?

Back

If the rate of change between the values is constant, the function is linear. If the rate of change varies, the function is nonlinear.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the slope (m) of the line, which represents how much y changes for a unit change in x.

Front

Write an equation for a function where the distance d is a function of time t, with a constant speed of 80 km/h.

Back

d = 80t.

Front

Write an equation for a function where the total cost y is a function of the number of additional family members x, with a base charge of $40 and $10 per additional member.

Back

y = 10x + 40.

Front

What does the slope of a line represent in a linear function?

Back

The slope represents the rate of change of the function, indicating how much the output (y) changes for a unit change in the input (x).

Front

If a function has a slope of -0.8, what does this indicate about the function's behavior?

Back

A slope of -0.8 indicates that for every 1 unit increase in x, the value of y decreases by 0.8 units, showing a negative relationship.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the value of y when x is 0, representing where the line crosses the y-axis.