Indep/dep variables
In the equation: "A car travels 60 miles per hour," what is the independent variable?
Time (hours)
What does the domain of a function tell you?
All the possible x-values (inputs) of the function.
A graph passes the vertical line test. What does this mean?
It is a function (passes the test).
What type of function is represented by a straight horizontal line?
A Constant Function
What do we call the point where a graph crosses the y-axis?
The y-intercept
You earn $15 per hour babysitting. What is the dependent variable?
Money earned
What does the range of a function tell you?
All the possible y-values (outputs) of the function.
Can a vertical line represent a function?
No
What type of function is y=x2?
Quadratic Function
What part of the graph tells you the highest or lowest point of a function?
The vertex
Absolute Max and Absolute Min
Identify the independent variable: "The height of a plant depends on how much sunlight it receives."
Amount of sunlight
A function is defined by the set of points: {(–2, 4), (0, 3), (3, 1), (4, –2)}. What is the range?
{4, 3, 1, –2}
Does the set {(1, 7), (2, 0), (3, 0)} represent a function?
Yes
What type of function is y=(x+3)-5
Linear Function
A parabola opens downward and its vertex is at (2, 5). What is the maximum value of the function?
5
A recipe uses 2 cups of sugar for every 5 cups of flour. Which is the dependent variable?
Cups of sugar
What is the range of (y =x)
All real numbers
Negative infinty to Positive infinity
Does the relation {(5, 7), (6, 8), (5, 9)} represent a function? Why or why not?
No, because 5 maps to two different outputs
What type of function makes a graph shaped like a “V”?
Absolute value function
What is the vertex for y=x2
(0,0)
A scientist records the growth of bacteria over 10 days in different temperatures. What are both variables, and which is independent?
Independent: Temperature; Dependent: Bacteria growth
A graph of a function starts at the point (–3, 2) and ends at the point (4, 6). It is a straight line that connects those points. What is the domain and range?
*Both start and end values are included
Domain: [–3, 4]
Range: [2, 6]
A vending machine gives a snack based on the code you enter. If you enter the same code, you always get the same snack. If every code gives one snack, but two different codes can give the same snack, is this a function? Why or why not?
Yes, this is a function because each input (code) gives exactly one output (snack). It's okay if multiple inputs give the same output — a function only requires one output per input.
Using all three types of functions from this list, match them to their graph shapes and equations: linear, quadratic, and absolute value.
Linear: line (diagonal), y=x;
Quadratic: U-shaped (parabola), x2;
Absolute Value: V-shape, y=|x|
What is the axis of symmetry of the graph y=x2
x=0