#1 Linear vs Exponential Intro

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, represented by a straight line, while exponential functions have a variable rate of change, represented by a curve that increases or decreases rapidly.

Front

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

Back

A linear function will show a constant difference between consecutive y-values for equal increments in x-values.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the growth factor in an exponential function?

Back

The growth factor is the constant multiplier that is applied to each value in the function, indicating how much the function grows or decays.

Front

How do you determine if a graph represents exponential growth?

Back

A graph represents exponential growth if it rises sharply and continuously increases without bound as x increases.

Front

What does a decay in an exponential function look like on a graph?

Back

Decay in an exponential function is represented by a graph that decreases rapidly and approaches zero but never actually reaches it.

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the value of y when x is zero.

Front

How can you tell if a function is exponential from its equation?

Back

A function is exponential if it can be expressed in the form y = ab^x, where a is a constant, b is the base (a positive number), and x is the exponent.

Front

What is a common characteristic of linear functions in terms of their slope?

Back

Linear functions have a constant slope, meaning the rate of change is the same between any two points on the line.

Front

What does it mean for a function to have a constant growth rate?

Back

A constant growth rate means that the function increases by the same amount over equal intervals of the independent variable.