Module A: Functions Flashcards
What is function notation?
Using f(x) = to name a function, where x is the input and f(x) is the output.
What is evaluating?
Evaluating is substituting an input to find an output
List the steps to evaluate f(3) for f(x) = 3x-5
- Substitute 3 for x: f(3) = 3(3)-5
- Multiply 3*3: f(3) = 9-5
- Combine terms: f(3) = 4
What are the four representations of a function?
EGTC: Equation, Graph, Table, & Context
If f(3) = 5, what do you see on a graph?
The coordinate (3,5)
x | 0 1 2 3 4
y | 4 7 10 13 16
What is the domain?
The domain is 0, 1, 2, 3, & 4
x | 0 1 2 3 4
y | 4 7 10 13 16
What is the range?
The range is 4, 7, 10, 13, & 16
What is a function?
A relation where each input has exactly one output.
Domain
The set of all x-values (inputs) of a function.
Range
The set of all y-values of a function
What types of values do not apply to domain & range in context?
Negative values for time (domain), negative values for measurements (range), etc…
What is an x-intercept?
The place where a graph crosses the x-axis. It is also called a root or a zero. For every x-intercept, y = 0.
What is a y-intercept?
The number on the y-axis where a function crosses. For every y-intercept, x = 0.
Maximum
The highest point on a graph. It has the largest y-value.
Minimum
The lowest point on a graph. It has the smallest y-value.
Average Rate of Change
The change in y-values divided by the change in their x-values.
(y2 - y1) / (x2 - x1)
How do you solve equations algebraically?
Use inverse operations
Classify the equation: f(x) = -2x + 7
Linear Equation
List the steps to solve the two-step equation: 4x - 9 = 11
- Invert -9 with + 9 on both sides: 4x = 20
2. Invert 4* by /4 on both sides: x = 5
List the steps to solve the inequality: 3 - 2x > - 7
- Subtract 3: -2x > -10
2. Divide by -2 (YOU MUST FLIP SIGN): x < 5
List the steps to solve the equation for A: Ax + By = C
- Subtract By: Ax = C - By
2. Divide by x: A = (C - By) / x
