Create Functions from Tables & Graphs

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as an equation, a table, or a graph.

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 a constant, 'b' is the base, and 'x' is the exponent.

Front

How do you determine the equation of a line from a graph?

Back

To determine the equation of a line from a graph, identify the slope (rise over run) and the y-intercept (where the line crosses the y-axis). Use the slope-intercept form: y = mx + b.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is a y-intercept?

Back

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

Front

How can you write a function from a table of values?

Back

To write a function from a table, look for patterns in the x and y values. Determine if the relationship is linear, quadratic, or exponential, and then derive the function.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change and are represented by straight lines, while exponential functions have a variable rate of change and are represented by curves.

Front

What is the equation of a line with a slope of -3 and a y-intercept of -3?

Back

The equation of the line is y = -3x - 3.

Front

How do you find the slope from two points?

Back

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the equation of a line with a slope of (3/5) and a y-intercept of 1?

Back

The equation of the line is y = (3/5)x + 1.