Unit 1 review - modeling 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) of a linear function is the point where the graph intersects the y-axis. It represents the value of the function when x = 0.

Front

How do you evaluate a linear function at a specific point?

Back

To evaluate a linear function f(x) = mx + b at a specific point x = a, substitute a into the function: f(a) = ma + b.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you find the domain of a linear function?

Back

For linear functions, the domain is typically all real numbers unless specified otherwise by a context (e.g., a real-world scenario).

Front

What does it mean for a function to be constant?

Back

A constant function is a linear function where the slope is zero (m = 0), resulting in a horizontal line. The output value remains the same regardless of the input.

Front

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

Back

A negative slope indicates that as the input (x) increases, the output (y) decreases. This represents an inverse relationship between x and y.

Front

How can you determine if a function is linear from a graph?

Back

A function is linear if its graph forms a straight line. You can also check if it can be expressed in the form f(x) = mx + b.