Embedded Files
Use the search feature to find content (and happiness!)
Major Ideas in Algebraic Functions (8th Grade)
Major Ideas in Algebraic Functions (8th Grade)
1. Relation
A relation is any set of ordered pairs that shows a connection between two things.
The first part of each pair is the input (x-value).
The second part of each pair is the output (y-value).
Example: {(2, 5), (3, 7), (4, 9)} is a relation. Here, 2 goes with 5, 3 goes with 7, and 4 goes with 9.
2. Function
2. Function
A function is a special type of relation where each input (x-value) has exactly one output (y-value).
3. Input and Output
Input: the value you put into a function (often called x).
Output: the value the function gives back (often called y).
4. Function Notation
Functions are often written like this: f(x) = 2x - 3.
This means “the function f of x equals 2 times x minus 3.”
The equation for this function is f(x) = 2x - 3.
4. Domain
The set of all possible input values (x-values) that make sense for the function.
6. Range
The set of all possible output values (y-values) the function can produce.
7. Linear Function
A function whose graph is a straight line. It can be written in the form y = mx + b, where:
y = output or answer
m = slope (steepness) positive or negative
x = input or step
b = y-intercept (where the line crosses the y-axis). Start.
The slope-intercept form of a linear equation is y = mx + b
y = - 2/3x + 5
f(x) = - 2/3x + 5
9. Nonlinear Function
A function whose graph is not a straight line (like parabolas, curves, or exponential graphs).
10. Independent Variable
The variable you choose or control (usually x). In this example, time is the independent variable.
11. Dependent Variable
The variable that depends on the independent variable (usually y). The dependent variable is the growth of the tree measured in feet.
12. Graph of a Function =
A picture that shows all the input–output pairs (x, y).
13. Vertical Line Test
A way to check if a graph represents a function: if a vertical line touches the graph more than once, it is not a function.
14. Rate of Change
How much the output changes compared to how much the input changes. For linear functions, this is the slope.
15. Slope (m)
The steepness of a line, found by rise ÷ run (change in y ÷ change in x).
16. X-Intercept
The point where the graph crosses the x-axis.
17. Y-Intercept (b)
The point where the graph crosses the y-axis.
18. Quadratic Function
A nonlinear function with the form y = ax² + bx + c. Its graph is a U-shaped curve called a parabola.
Report abuse