Linear 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 does the slope of a linear function represent?

Back

The slope (m) of a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

Front

What is the y-intercept of a linear function?

Back

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

Front

Evaluate f(-2) if f(x) = x + 3.

Back

f(-2) = -2 + 3 = 1.

Front

Evaluate f(3) if f(x) = 1/3x + 6.

Back

f(3) = 1/3(3) + 6 = 1 + 6 = 7.

Front

How do you model a situation with a linear function?

Back

Identify the initial value and the rate of change. Use the form y = mx + b, where m is the rate of change and b is the initial value.

Front

What is the function that models Bob's savings if he starts with $150 and saves $40 per month?

Back

y = 40x + 150, where y is the total savings after x months.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input. Each input must have a unique output.

Front

What does it mean if a relation is not a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

How can you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.