What is a function?
Vertical Line Test Are these graphs functions? 1
3
2
4
On your own‌. On the following web page, connect the given points to try and form a function. Complete ten sets of points. Creating functions
Y = mx + b Standard form of a line Y = mx + b Y= m= x= b=
Identify the slope and y-intercept in each equation.
Y = 4x + 8
Y = 3x – 4
Y = -2x
Y = 10
Graphing equations
Start with the yintercept Use the slope to find a second point Two points form a line, now we can draw our graph! Does the graph make sense?
Y = 2x – 5 What is the y-intercept? Plot the point! What is the slope? Start from the y-intercept and plot the second point!
Graph each equation (on your own) 1. 2. 3. 4. 5. 6. 7.
Y = (1/2)x + 4 Y=x Y = 3x Y=9 X=3 3x + y = 4x – 8 3 – y = 2x + 10
Partner work 1.
Go to this web page and graph the following equations: Graphing linear equations Y = 6x – 8 d) 3x + 7 = y – x b) Y = (3/4)x + 5 e) y = 5.5 c) X=8 f) y + 3x = (1/2) Sketch each graph on your paper. Put each equation in y = mx+b for (if needed) a)
2. 3. 4.
What makes these equations linear? Can you think of a graph that would be nonlinear? Sketch an example. Are all of these equations functions? Why or why not?
Solving for m and b After you turn in your partner work, use the “Function Machine� to try and solve for m and b in your y = mx + b equation. You may work with partners. For each equation you solve, you can earn one extra credit point! On your paper, you must include all the points you plugged into the machine (x, y values) and the equation you came up with! Function Machine