Linear and Exponential Functions

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

How do you identify the y-intercept in a function?

Back

The y-intercept is the value of y when x is 0. In the function f(x) = a(b^x), the y-intercept is the initial value 'a'.

Front

What does the equation y = mx + b represent?

Back

This is the slope-intercept form of a linear equation, where 'm' is the slope and 'b' is the y-intercept.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change (slope), while exponential functions have a variable rate of change that increases or decreases multiplicatively.

Front

How can you determine if a graph is linear or exponential?

Back

A linear graph forms a straight line, while an exponential graph curves upwards or downwards.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a(b^x), where 'a' is the initial value and 'b' is the growth (b > 1) or decay (0 < b < 1) factor.

Front

How do you find the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line descends from left to right.

Front

What is the y-intercept of the function f(x) = 5x + 3?

Back

The y-intercept is 3, which is the value of f(x) when x = 0.

Front

What is the equation of a line with a slope of 2 and a y-intercept of -1?

Back

The equation is y = 2x - 1.