Exploring Graphing Functions with UF4 Guided Notes

The video tutorial covers graphing functions, starting with an introduction to graphing using a given domain. It explains how to solve for y and plot points for specific x values, distinguishing between discrete and continuous graphs. The tutorial then explores graphing with all real numbers and demonstrates using the Desmos app for graphing functions. Finally, it applies graphing concepts to model real-world situations, emphasizing the importance of understanding domains and ranges.

What is the first step in solving for y in the equation x + 3y = 15?

• Add x to both sides

• Subtract x from both sides

• Multiply both sides by 3

• Divide both sides by 3

If x is 6 in the equation y = -1/3x + 5, what is the value of y?

• 5

• 3

• 2

• 4

Why should you not connect the points in a discrete graph?

• Because the range is infinite

• Because the domain is limited to specific values

• Because the graph is a parabola

• Because the points represent a continuous function

What would the graph look like if the domain was from 0 to 9 and included all values in between?

• A line segment

• A set of discrete points

• A parabola

• A circle

What is the purpose of drawing arrowheads at both ends of a graph?

• To show the graph is a discrete function

• To indicate the graph is a parabola

• To mark the endpoints of the graph

• To represent an infinite number of ordered pairs

In the function f(x) = 3x - 5, what is the value of f(1)?

• 1

• -2

• 4

• 7

What tool can be used to graph functions and trace values?

• Desmos

• Calculator

• Excel

• GeoGebra

When using Desmos, what is the y-value when x is -2 for the function y = -1/2x + 3?

• 2

• 3

• 1

• 4

In modeling real-world situations, why do we often use non-negative domains and ranges?

• Because it is easier to plot

• Because negative values are not realistic in many contexts

• Because it simplifies the calculations

• Because it makes the graph look better

If a cruise ship travels according to the function y = 15x + 5, how far is it from port after 2 hours?

• 50 km

• 35 km

• 30 km

• 20 km