Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs.

Front

How do you determine the slope of a linear function?

Back

The slope of a linear function is determined by the change in the y-values divided by the change in the x-values between two points on the line.

Front

What does a steeper slope indicate about a function?

Back

A steeper slope indicates a greater rate of change; the function increases or decreases more rapidly.

Front

What is the initial value of a function?

Back

The initial value of a function is the output value when the input is zero, often represented as the y-intercept in a linear function.

Front

How can you compare the rates of change of two functions?

Back

You can compare the rates of change by examining the slopes of the functions; the function with the larger slope has a greater rate of change.

Front

What does it mean if two functions have different initial values?

Back

It means that the starting points of the functions on the y-axis are different when the input (x) is zero.

Front

How do you interpret the growth of a plant represented by a linear function?

Back

The growth of a plant represented by a linear function can be interpreted by analyzing the slope, which indicates the rate of growth over time.

Front

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

Back

The coefficients in a linear function determine the slope and the initial value; the coefficient of x represents the rate of change, while the constant term represents the initial value.

Front

How can you visually compare two functions on a graph?

Back

You can visually compare two functions by plotting them on the same graph and observing their slopes and initial values.

Front

What does it mean for one function to grow faster than another?

Back

It means that the function has a greater slope, indicating a higher rate of change over the same interval.