Examples
Assume you need 12.6 gallons to fill up your car. Now, one of the variables is a constant, which means the value will not vary throughout the problem.
Let's say I give you the price per gallons of: 3.00 3.50 4.00 4.50 and 5.00 find the cost of fill up
Is the cost of a fill up a function of the price per gallon? Explain.
37.80 44.10 50.40 56.70 63.00
Yes, for each value of input, there is one output
Solve for 3x+90=120
x=10
A set of two numbers written in the form (x,y) where x is the input and y is the output
ordered pair
a scatterplot
a ______ function that is defined for all input values with no gaps in between
Continuous function
At midnight, the building temperature is 55 degrees F. This temperature remains constant until 4 am., at which time the temperature of the building begins a steady increase. By 7am, the temperature is 68 degrees F, and the building is maintained at this temperature until 7pm. when the temperature begins a steady decrease. By 10 pm, the temperature is back to 55 degrees F. What should you do?
Sketch a graph
Solve for 2/3x-12=2
x=21
The average rate of change is another word for
An example of a continuous function graph would be a
one continuous line
a _____ function that is defined for isolated, distinct input values
Discrete function
Graph l1: (-2,-3), (2,5)
Graph l2: (-1,-5), (3,3)
Graph on the board or piece of paper
What is the equation for slope-intercept form?
y=mx+b
the collection of all possible values for the input variable
domain
If I have a sideways V graphed on a graph, and I asked you to perform a vertical line test. Would that graph be a function?
No
If I have the function f(x)= x2 what does the graph look like?
Parabola
Write the slope intercept form of the line that contains the given points: (-7,1) and (-5,-3)
y=-2x-13
What is the equation for standard form?
Ax+By=C
this test is used to determine whether a graph represents a function
vertical line test
What happens with a vertical or horizontal shift?
V: moves the graph up or down
H: moves the graph left or right
If I have a function that is f(x)=lxl, what does my graph look like?
V
A university requires that students applying for admission must have a combined SAT verbal and math score of at least 1200. The college of arts and sciences has an additional requirement that the verbal score must be at least 600. The maximum score on each part of the SAT is 800. Write the requirements of the problem as inequalities and use a graph to find the solution to the system
Solve on board or piece of paper
What is the equation for point-slope form?
y-y1=m(x-x1)
a real number that cannot be expressed as a quotient of two integers
irrational
y-16=8(x-5)
Put this into slope-intercept form and the graph it
y=8x-24
Proceed to graph
If I have a graph that has a hill and a valley, I'll draw an example on board, is it a function?
Yes