Independent/dependent variables
Identify the independent variable: The relationship between the number of hours worked and the amount of money earned.
The number of hours worked
Is this set of points a function? (2, 5) (1,3) (-1, -1) (-2, -3)
Yes, these points make up a function because each input has 1 output
f(x) = -2x - 11
find x when f(x) = 41
x = -26
f(x) = -5x + 13
find f(3)
f(3) = -2
Identify the dependent and independent variables: On your math homework, you earn 5 points for each question that you answer correctly.
Dependent: Your score on the homework
Independent: the number of questions you answer correctly
Does the graph of the points (1,3) and (1,5) represent a function?
No, because this input has more than 1 output (these points fail the vertical line test)
f(x)=x^2 - 9
find f(-6)
f(-6) = 27
f(x) = -20 + 11x
find f(11)
f(11) = 101
Identify the independent and dependent variables: You are buying a box of cookies at a bakery. Each cookie costs $1.25.
Independent: The number of cookies you bought
Dependent: the total cost of the box of cookies
Is this set of points a function? (2,4), (1,5), (2,6)
No, the input 2 has more than one output (4 and 6)
f(x) = 25 - 3x
find f(4)
f(4) = 13
f(x) = 6x + 100
find f(-5)
f(-5) = 70
Identify the independent and dependent variables: you and some of your friends are at a restaurant. Some of your friends order soda, for $3 each.
Dependent: how much money is spent on soda
Is the set of points a function? (2, -4) (4,-4) (6, 5) (8, 5)
Yes, each input has exactly 1 output
f(x) = 50 - (x/5)
find f(35)
f(35) = 43
f(x)=25 - 4x
find x when f(x) = 9
x = 4