Science Experiment’s The Dependent and Independent Variable Experimental Group Control Group

Independent Variable Scientist controls whether or not subjects are exposed to this It is manipulated Air pressure might be increased or decreased Water flow might be increased or decreased Time might be increased or decreased Age of people Number of people Changed by scientist Usually only one Graphed on X axis

Dependent Variable What are you measuring? What will change? What effect will the independent variable have on this? What are the results? What Happened? Also called the responding variable

Thinking Algebraically The input of a function is the independent variable. The output of a function is the dependent variable. The value of the dependent variable depends on, or is a function of, the value of the independent variable.

Experimental Group This is the group or thing you want to test. Something is done to this group or thing. You can say “ see this group, we did X,Y, and Z to this group and look what happened.

Control Group Nothing is done to this group. You can say, “ see this group, we didn’t do anything to them and look at what happened”

Examples of Independent and Dependent Variables A painter must measure a room before deciding how much paint to buy. The amount of paint depends on the measurement of a room. Dependent: amount of paint Independent: measurement of the room Dependent Variable Amount of paint Independent Variable Measurement of room

Dependent Variable is Height of candle Example The height of a candle decrease d centimeters for every hour it burns. The height of a candle depends on the number of hours it burns. Dependent: Height of candle Independent: Time Independent Variable Time candle burns Dependent Variable is Height of candle

The amount of medication depends on the weight of an animal. A veterinarian must weigh an animal before determining the amount of medication. The amount of medication depends on the weight of an animal. Dependent: amount of medication Independent: weight of animal Independent Variable Weight of Animal Dependent Variable Amount of medication

Writing Functions A function relates an input to an output It is like a machine that has an input and an output. And the output is related somehow to the input. There are several different ways to describe the variables of a function. Independent Dependent Variable Variable x-values y-values Domain Range Input Output X f(x)

A function of X is: f(x) A function of the dependent variable is the independent variable A company charges $10 per hour to rent a jackhammer. A function of time is cost The cost to rent a jackhammer depends on the length of time it is rented. Dependent variable: cost Independent variable: time

The Function Machine Output F(X) Input (X) Dependent Variable Read: “f of X” Input (X) Independent Variable

How the function machine works Example: this tree grows 20 cm every year, so the height of the tree is related to its age using the function h: h(age) = age × 20 So, if the age is 10 years, the height is: h(10) = 10 × 20 = 200 cm Here are some example values: A function relates each element of a set with exactly one element of another set (possibly the same set). Input (x) age H (age) h = 20 cm Output 1 1 x 20 cm 20 3 3 x 20 cm 60 5 5 x 20 cm 100 7 7 x 20 cm 140 9 9 x 20 cm 180

Example Question: Does air pressure in tires affect gas mileage? Answer: Yes gas mileage is lower if tires are not full of air. Low tire pressure results in poor gas mileage. Air pressure is the independent variable and gas mileage is the dependent variable. Gas mileage depends on air pressure

Example Number of gallons to flow out of a faucet at constant water pressure depends on water flow, i.e. is the faucet open al the way or only a little. Independent Variable is: Water Flow Dependent Variable is: Number of gallons How many gallons of water will flow out of faucet with constant water pressure and with the water faucet open all the way depends on the amount of time. Independent Variable: Time Dependent Variable: Number of Gallons

The independent variable is always graphed on the X axis. Usually the manipulated, independent, variable is written on the left but not always. The independent variable is always graphed on the X axis. Length of Drop (cm) Independent Variable Height of bounce (cm) Dependent Variable 10 8 30 24 50 40 70 56 100 80

Example X axis is cause Y axis is effect