Questions and Answers
What is an equation?
A mathematical sentence that contains an equals sign and shows that two statements are the same.
What is an expression?
A mathematical phrase that contains operations, numbers, and/or variables, and does not have an equal sign.
What is an inequality?
A mathematical sentence that shows the relationship between quantities that are not the same, containing the symbols <, ≤, ≥, or ≠.
What kind of circle and arrow would a < (less than) inequality have when graphing?
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What kind of circle and arrow would a ≥ (greater than or equal to) inequality have when graphing?
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What are rational numbers?
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What are integers?
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What are integers greater than or equal to zero?
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What are rational numbers greater than or equal to zero?
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What is the domain of a function?
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What is a function?
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What does f(x) stand for?
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If given f(3), what should you do?
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If given f(x)=3, what should you do?
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What are real numbers?
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What is a linear function?
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What is an increasing function?
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What is a decreasing function?
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What are solutions to an equation?
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What is an x-intercept?
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What is a y-intercept?
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How do you find the x-intercept of an equation algebraically?
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How do you find the y-intercept of an equation algebraically?
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What is the rate of change?
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What is slope?
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What does the graph of an equation of the form x = # look like?
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What does the graph of an equation of the form y = # look like?
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What button(s) do you press on your calculator to graph an equation?
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What button(s) do you press on your calculator to look at a table after you've typed the equation?
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What button(s) do you press on your calculator to create a fraction?
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What button(s) do you press on your calculator to change a decimal to a fraction?
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Where is the solution to a system of equations on a graph?
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What is a system of equations?
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What is a system of inequalities?
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Study Notes
Vocabulary and Definitions
- Equation: A mathematical sentence with an equals sign that indicates two statements are equivalent.
- Expression: A mathematical phrase combining operations, numbers, and/or variables without an equals sign.
- Inequality: A mathematical sentence indicating a relationship between unequal quantities using symbols like <, ≤, ≥, and ≠.
Graphing Inequalities
- Less than (<) Inequality: Represented by an open circle and an arrow pointing left.
- Greater than or equal to (≥) Inequality: Depicted by a closed circle with an arrow pointing right.
Types of Numbers
- Rational Numbers: Includes all positive and negative integers, fractions, and decimal numbers.
- Integers: The set of whole numbers including their negatives: {..., -2, -1, 0, 1, 2, ...}.
- Non-negative Integers: All whole numbers greater than or equal to zero.
- Non-negative Rational Numbers: Includes all positive integers, fractions, and decimal numbers.
Functions and Their Properties
- Domain of a Function: Comprises all possible x-values for that function.
- Function: A relation where each x-value corresponds to one unique y-value, pass the Vertical Line Test.
- Notation f(x): Represents the y-value of the function corresponding to x.
Function Evaluation
- To find f(3): Substitute 3 for x in f(x).
- To find f(x)=3: Substitute 3 for y in the function.
Types of Numbers Continued
- Real Numbers: All numbers, encompassing both rational and irrational numbers.
- Linear Function: An equation producing a straight line graph, characterized by a maximum exponent of 1.
Function Behavior
- Increasing Function: A graph that rises from left to right.
- Decreasing Function: A graph that falls from left to right.
Solutions and Intercepts
- Solutions to an Equation: Ordered pairs that satisfy the original equation, represented graphically on the function's graph.
- X-Intercept: The point where the graph intersects the x-axis (y=0).
- Y-Intercept: The point where the graph intersects the y-axis (x=0).
Finding Intercepts Algebraically
- X-Intercept: Found by setting y = 0 and solving for x.
- Y-Intercept: Found by setting x = 0 and solving for y.
Additional Concepts
- Rate of Change: Indicates how a quantity changes over time, calculated with the same formula as slope.
- Slope: Defined as the ratio of rise to run in a linear function.
Graphing Techniques
- Graph of x = #: A vertical line representation.
- Graph of y = #: A horizontal line representation.
Calculator Functions
- Graphing an Equation: Press [y =], input the equation, and then hit [graph].
- Viewing a Table: After entering the equation, press [2ND] [GRAPH].
- Creating a Fraction: Use the division sign [÷].
- Converting a Decimal to a Fraction: Use [MATH] [ENTER] [ENTER].
Solving Systems
- Solution to a System of Equations: Identified at the point where the graphs intersect.
- System of Equations: Consists of two or more equations with common variables, solved simultaneously.
- System of Inequalities: Comprises two or more inequalities sharing the same variables.
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Test your understanding of key vocabulary in Algebra 1 with these flashcards. Learn definitions such as 'equation', 'expression', and 'inequality' to enhance your mathematical language skills. Perfect for NJ-SLA students looking to solidify their knowledge!