3.4 Graphing Functions

A snowboarder's elevation, in feet, can be represented by the function E(t) = 3000 - 70t, where t is in seconds. Find the elevation of the snowboarder after 30 seconds.

A: E(30) = 3000 - 70(30) E(30) = 3000 - 2100 E(30) = 900 After 30 seconds, the snowboarder is at about 900 feet.

Solve f(x) when x = 3 f(x) = 3x -5

A: f(3) = 3(3) - 5 f(3) = 4

What is the benefit of solving for y (rewriting an equation in the form of y = ...) before graphing a function?

It is easier to substitute values for x and solve for the corresponding y-values when the equation has been solved for y

How could you use a graph to find the value of x for which f(x) equals a given value?

Locate the given value of f(x) on the y-axis. Draw a horizontal line segment from there to the graph of the function, then draw a vertical line segment to the x-axis to find the correspond x-value.

What is "The Function Machine?"

a visual organizer for keeping track of inputs and outputs of a function rule

Domain of All Real Numbers

graph will be a continuous graph (smooth line or curve); if they domain is a specific set of numbers, the graph is a discrete graph (consisting of distinct points)

What are the steps for graphing a function?

1. solve for y 2. choose values for x (table of values) 3. generate ordered pairs (table of values) 3. graph ordered pairs

How do you graph functions?

You can use a table of values to generate ordered pairs - if the graph is discrete, plot only the points; if the graph is continuous, connect the points with a line or curve